{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reliable uncertainty estimates for neural network predictions\n",
    "\n",
    "I previously wrote about [Bayesian neural networks](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks.ipynb) and explained how uncertainty estimates can be obtained for network predictions. Uncertainty in predictions that comes from uncertainty in network weights is called *epistemic uncertainty* or model uncertainty. A simple regression example demonstrated how epistemic uncertainty increases in regions outside the training data distribution:\n",
    "\n",
    "![Epistemic uncertainty](images/epistemic-uncertainty.png)\n",
    "\n",
    "A reader later [experimented](https://github.com/krasserm/bayesian-machine-learning/issues/8) with discontinuous ranges of training data and found that uncertainty estimates are lower than expected in training data \"gaps\", as shown in the following figure near the center of the $x$ axis. In these out-of-distribution (OOD) regions the network is over-confident in its predictions. One reason for this over-confidence is that weight priors usually impose only weak constraints over network outputs in OOD regions.\n",
    "\n",
    "![Epistemic uncertainty gap](images/epistemic-uncertainty-gap.png)\n",
    "\n",
    "If we could instead define a prior in data space directly we could better control uncertainty estimates for OOD data. A prior in data space better captures assumptions about input-output relationships than priors in weight space. Including such a prior through a loss in data space would allow a network to learn distributions over weights that better generalize to OOD regions i.e. enables a network to output more reliable uncertainty estimates.\n",
    "\n",
    "This is exactly what the paper [Noise Contrastive Priors for Functional Uncertainty](http://proceedings.mlr.press/v115/hafner20a.html) does. In this article I'll give an introduction to their approach and demonstrate how it fixes over-confidence in OOD regions. I will again use non-linear regression with one-dimensional inputs as an example and plan to cover higher-demensional inputs in a later article. \n",
    "\n",
    "Application of noise contrastive priors (NCPs) is not limited to Bayesian neural networks, they can also be applied to deterministic neural networks. Here, I'll use a Bayesian neural network and implement it with Tensorflow 2 and [Tensorflow Probability](https://www.tensorflow.org/probability)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import logging\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from tensorflow.keras.layers import Input, Dense, Lambda, LeakyReLU\n",
    "from tensorflow.keras.models import Model\n",
    "from tensorflow.keras.regularizers import L2\n",
    "from tensorflow_probability import distributions as tfd\n",
    "from tensorflow_probability import layers as tfpl\n",
    "from scipy.stats import norm\n",
    "\n",
    "from utils import (train,\n",
    "                   backprop,\n",
    "                   select_bands, \n",
    "                   select_subset,\n",
    "                   style,\n",
    "                   plot_data, \n",
    "                   plot_prediction, \n",
    "                   plot_uncertainty)\n",
    "\n",
    "%matplotlib inline\n",
    "logging.getLogger('tensorflow').setLevel(logging.ERROR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training dataset are 40 noisy samples from a sinusoidal function `f` taken from two distinct regions of the input space (red dots). The gray dots illustrate how the noise level increases with $x$ (heteroskedastic noise). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    \"\"\"Sinusoidal function.\"\"\"\n",
    "    return 0.5 * np.sin(25 * x) + 0.5 * x\n",
    "\n",
    "\n",
    "def noise(x, slope, rng=np.random):\n",
    "    \"\"\"Create heteroskedastic noise.\"\"\"\n",
    "    noise_std = np.maximum(0.0, x + 1.0) * slope\n",
    "    return rng.normal(0, noise_std).astype(np.float32)\n",
    "\n",
    "x = np.linspace(-1.0, 1.0, 1000, dtype=np.float32).reshape(-1, 1)\n",
    "x_test = np.linspace(-1.5, 1.5, 200, dtype=np.float32).reshape(-1, 1)\n",
    "\n",
    "# Noisy samples from f (with heteroskedastic noise)\n",
    "y = f(x) + noise(x, slope=0.2, rng=rng)\n",
    "\n",
    "# Select data from 2 of 5 bands (regions)\n",
    "x_bands, y_bands = select_bands(x, y, mask=[False, True, False, True, False])\n",
    "\n",
    "# Select 40 random samples from these regions\n",
    "x_train, y_train = select_subset(x_bands, y_bands, num=40, rng=rng)\n",
    "\n",
    "plot_data(x_train, y_train, x, f(x))\n",
    "plt.scatter(x, y, **style['bg_data'], label='Noisy data')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Goal is to have a model that outputs lower epistemic uncertainty in training data regions and higher epistemic uncertainty in all other regions, including training data \"gaps\". In addition to estimating epistemic uncertainty the model should also estimate *aleatoric uncertainty* i.e. the heteroskedastic noise in the training data. \n",
    "\n",
    "## Noise contrastive estimation\n",
    "\n",
    "The algorithm developed by the authors of the NCP paper is inspired by [noise contrastive estimation](http://proceedings.mlr.press/v9/gutmann10a.html) (NCE). With noise contrastive estimation a model learns to recognize patterns in training data by contrasting them to random noise. Instead of training a model on training data alone it is trained in context of a binary classification task with the goal of discriminating training data from noise data sampled from an artificial noise distribution. \n",
    "\n",
    "Hence, in addition to a trained model, NCE also obtains a binary classifier that can estimate the probability of input data to come from the training distribution or from the noise distribution. This can be used to obtain more reliable uncertainty estimates. For example, a higher probability that an input comes from the noise distribution should result in higher model uncertainty.\n",
    "\n",
    "Samples from a noise distribution are often obtained by adding random noise to training data. These samples represent OOD data. In practice it is often sufficient to have OOD samples *near* the boundary of the training data distribution to also get reliable uncertainty estimates in other regions of the OOD space. Noise contrastive priors are based on this hypothesis.\n",
    "\n",
    "## Noise contrastive priors\n",
    "\n",
    "A noise contrastive prior for regression is a joint *data prior* $p(x, y)$ over input $x$ and output $y$. Using the product rule of probability, $p(x, y) = p(x)p(y \\mid x)$, it can be defined as the product of an *input prior* $p(x)$ and an *output prior* $p(y \\mid x)$. \n",
    "\n",
    "The input prior describes the distribution of OOD data $\\tilde{x}$ that are generated from the training data $x$ by adding random noise epsilon i.e. $\\tilde{x} = x + \\epsilon$ where $\\epsilon \\sim \\mathcal{N}(0, \\sigma_x^2)$. The input prior can therefore be defined as the convolved distribution:\n",
    "\n",
    "$$\n",
    "p_{nc}(\\tilde{x}) = {1 \\over N} \\sum_{i=1}^N \\mathcal{N}(\\tilde{x} - x_i \\mid 0, \\sigma_x^2)\n",
    "\\tag{1}\n",
    "$$\n",
    "\n",
    "where $x_i$ are the inputs from the training dataset and $\\sigma_x$ is a hyper-parameter. As described in the paper, models trained with NCPs are quite robust to the size of input noise $\\sigma_x$. The following figure visualizes the distribution of training inputs and OOD inputs as histograms, the orange line is the input prior density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def perturbe_x(x, y, sigma_x, n=100):\n",
    "    \"\"\"Perturbe input x with noise sigma_x (n samples).\"\"\"\n",
    "    ood_x = x + np.random.normal(scale=sigma_x, size=(x.shape[0], n))\n",
    "    ood_y = np.tile(y, n)    \n",
    "    return ood_x.reshape(-1, 1), ood_y.reshape(-1, 1)\n",
    "    \n",
    "def input_prior_density(x, x_train, sigma_x):\n",
    "    \"\"\"Compute input prior density of x.\"\"\"\n",
    "    return np.mean(norm(0, sigma_x).pdf(x - x_train.reshape(1, -1)), axis=1, keepdims=True)\n",
    "\n",
    "sigma_x = 0.2\n",
    "sigma_y = 1.0\n",
    "\n",
    "ood_x, ood_y = perturbe_x(x_train, y_train, sigma_x, n=25)\n",
    "ood_density = input_prior_density(ood_x, x_train, sigma_x)\n",
    "\n",
    "sns.lineplot(x=ood_x.ravel(), y=ood_density.ravel(), color='tab:orange');\n",
    "sns.histplot(data={'Train inputs': x_train.ravel(), 'OOD inputs': ood_x.ravel()}, \n",
    "                   element='bars', stat='density', alpha=0.1, common_norm=False)\n",
    "\n",
    "plt.title('Input prior density')\n",
    "plt.xlabel('x');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The definition of the output prior is motivated by *data augmentation*. A model should be encouraged to not only predict target $y$ at training input $x$ but also predict the same target at perturbed input $\\tilde{x}$ that has been generated from $x$ by adding noise. The output prior is therefore defined as:\n",
    "\n",
    "\n",
    "$$\n",
    "p_{nc}(\\tilde{y} \\mid \\tilde{x}) = \\mathcal{N}(\\tilde{y} \\mid y, \\sigma_y^2)\n",
    "\\tag{2}\n",
    "$$\n",
    "\n",
    "$\\sigma_y$ is a hyper-parameter that should cover relatively high prior uncertainty in model output given OOD input. The joint prior $p(x, y)$ is best visualized by sampling values from it and doing a kernel-density estimation from these samples (a density plot from an analytical evaluation is rather \"noisy\" because of the data augmentation setting)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def output_prior_dist(y, sigma_y):\n",
    "    \"\"\"Create output prior distribution (data augmentation setting).\"\"\"\n",
    "    return tfd.Independent(tfd.Normal(y.ravel(), sigma_y))\n",
    "\n",
    "def sample_joint_prior(ood_x, output_prior, n):\n",
    "    \"\"\"Draw n samples from joint prior at ood_x.\"\"\"\n",
    "    x_sample = np.tile(ood_x.ravel(), n)\n",
    "    y_sample = output_prior.sample(n).numpy().ravel()\n",
    "    return x_sample, y_sample\n",
    "\n",
    "output_prior = output_prior_dist(ood_y, sigma_y)\n",
    "x_samples, y_samples = sample_joint_prior(ood_x, output_prior, n=10)\n",
    "\n",
    "sns.kdeplot(x=x_samples, y=y_samples, \n",
    "            levels=10, thresh=0, \n",
    "            fill=True, cmap='viridis', \n",
    "            cbar=True, cbar_kws={'format': '%.2f'},\n",
    "            gridsize=100, clip=((-1, 1), (-2, 2)))\n",
    "plot_data(x_train, y_train, x, f(x))\n",
    "plt.title('Joint prior density')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression models\n",
    "\n",
    "The regression models used in the following subsections are probabilistic models $p(y \\mid x)$ parameterized by the outputs of a neural network given input $x$. All networks have two hidden layers with leaky ReLU activations and 200 units each. The details of the output layers are described along with the individual models. I will first demonstrate how two models without NCPs fail to produce reliable uncertainty estimates in OOD regions and then show how NCPs can fix that.\n",
    "\n",
    "### Deterministic neural network without NCPs\n",
    "\n",
    "A regression model that uses a deterministic neural network for parameterization can be defined as $p(y \\mid x, \\boldsymbol{\\theta}) = \\mathcal{N}(y \\mid \\mu(x, \\boldsymbol{\\theta}), \\sigma^2(x, \\boldsymbol{\\theta}))$. Mean $\\mu$ and standard deviation $\\sigma$ are functions of input $x$ and network weights $\\boldsymbol{\\theta}$. In a deterministic neural network, $\\boldsymbol{\\theta}$ are point estimates. Outputs at input $x$ can be generated by sampling from $p(y \\mid x, \\boldsymbol{\\theta})$ where $\\mu(x,\\boldsymbol{\\theta})$ is the expected value of the sampled outputs and $\\sigma^2(x, \\boldsymbol{\\theta})$ their variance. The variance represents aleatoric uncertainty. \n",
    "\n",
    "Given a training dataset $\\mathbf{x}, \\mathbf{y} = \\left\\{ x_i, y_i \\right\\}$ and using $\\log p(\\mathbf{y} \\mid \\mathbf{x}, \\boldsymbol{\\theta}) = \\sum_i \\log p(y_i \\mid x_i, \\boldsymbol{\\theta})$, a maximum likelihood (ML) estimate of $\\boldsymbol{\\theta}$ can be obtained by minimizing the negative log likelihood.\n",
    "\n",
    "$$\n",
    "L(\\boldsymbol{\\theta}) = - \\log p(\\mathbf{y} \\mid \\mathbf{x},\\boldsymbol{\\theta})\n",
    "\\tag{3}\n",
    "$$\n",
    "\n",
    "A maximum-a-posteriori (MAP) estimate can be obtained by minimizing the following loss function:\n",
    "\n",
    "$$\n",
    "L(\\boldsymbol{\\theta}) = - \\log p(\\mathbf{y} \\mid \\mathbf{x}, \\boldsymbol{\\theta}) - \\lambda \\log p(\\boldsymbol{\\theta})\n",
    "\\tag{4}\n",
    "$$\n",
    "\n",
    "where $p(\\boldsymbol{\\theta})$ is an isotropic normal prior over network weights with zero mean. This is also known as L2 regularization with regularization strength $\\lambda$.\n",
    "\n",
    "The following implementation uses the `DistributionLambda` layer of Tensorflow Probability to produce $p(y \\mid x, \\boldsymbol{\\theta})$ as model output. The `loc` and `scale` parameters of that distribution are set from the output of layers `mu` and `sigma`, respectively. Layer `sigma` uses a [softplus](https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Softplus) activation function to ensure non-negative output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_model(n_hidden=200, regularization_strength=0.01):\n",
    "    l2_regularizer = L2(regularization_strength)\n",
    "    leaky_relu = LeakyReLU(alpha=0.2)\n",
    "\n",
    "    x_in = Input(shape=(1,))\n",
    "    x = Dense(n_hidden, activation=leaky_relu, kernel_regularizer=l2_regularizer)(x_in)\n",
    "    x = Dense(n_hidden, activation=leaky_relu, kernel_regularizer=l2_regularizer)(x)\n",
    "    m = Dense(1, name='mu')(x)\n",
    "    s = Dense(1, activation='softplus', name='sigma')(x)\n",
    "    d = Lambda(lambda p: tfd.Normal(loc=p[0], scale=p[1] + 1e-5))((m, s))\n",
    "\n",
    "    return Model(x_in, d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = create_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To reduce overfitting of the model to the relatively small training set an L2 regularizer is added to the kernel of the hidden layers. The value of the corresponding regularization term in the loss function can be obtained via `model.losses` during training. The negative log likelihood is computed with the `log_prob` method of the distribution returned from a `model` call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def train_step(model, optimizer, x, y):\n",
    "    with tf.GradientTape() as tape:\n",
    "        out_dist = model(x, training=True)\n",
    "        nll = -out_dist.log_prob(y)\n",
    "        reg = model.losses\n",
    "        loss = tf.reduce_sum(nll) + tf.reduce_sum(reg)\n",
    "\n",
    "    optimizer.apply_gradients(backprop(model, loss, tape))\n",
    "    return loss, out_dist.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this specific regression model, we can only predict aleatoric uncertainty via $\\sigma(x, \\boldsymbol{\\theta})$ but not epistemic uncertainty. After training the model, we can plot the expected output $\\mu$ together with aleatoric uncertainty. Aleatoric uncertainty increases in training data regions as $x$ increases but is not reliable in OOD regions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1000: loss = 2.188, mse = 0.114\n",
      "epoch 2000: loss = -2.775, mse = 0.061\n",
      "epoch 3000: loss = -4.832, mse = 0.045\n",
      "epoch 4000: loss = -5.896, mse = 0.039\n"
     ]
    }
   ],
   "source": [
    "train(model, x_train, y_train, batch_size=10, epochs=4000, step_fn=train_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "out_dist = model(x_test)\n",
    "\n",
    "aleatoric_uncertainty=out_dist.stddev()\n",
    "expected_output = out_dist.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jAWAfamhoYOrUqS2vV199lbi4OH73u99xzz338Morr1BRUcH9998PQF1dHdOnT2fHjh0sXLiwJVh64IEH+O1vf8v27dv5+c9/3rK88zvf+Q4LFy5k9+7d7Nixg4suuoif/exnjB07ll27dvHUU0/xySefcPjwYbZs2cKuXbvYvn07a9euZfv27bzyyivs3LmTN998k61bt/p8hgcffJC77rqLPXv2cMcdd/Cd73yn02f+2c9+xoIFC9i1axcPPfQQAFu2bOGll15i165dvP7662zbts3v9TfddBP5+fkt7W22zvd1iaHNqZ00ehoxBVjdvnmtlVmX+C8ADxBpiAzl0IQQQggh+gXZA9iHmpeAtnf55Zfz+uuv861vfYvdu3e3HDcYDNxyyy0A3Hnnndxwww3U1tayYcMGbr755pZ2drsdgM8++4wXXngB8O43jIuLo6Kiok1fn3zyCZ988gnTpk0DoLa2lsOHD1NTU8P1119PZKT3h95rr73W5zNs3LiRN998E4CvfOUr/Mu//EuX/x0uv/xykpKSALjhhhtYt24dX/rSl7p8HyHaa/A0oNGd7v/zeGDL5zb+9Sn/+/9QyP4/IYQQQgxKQzYA7I3SXt3N1OvxeDhw4AA2m43y8nK/WXyUUng8HuLj430GksGNUfPDH/6Qr3/9622O//rXv+5WvbPma0wmEx6Pp6UPh8MR8JrW71tfD9DY2PnsjBC+VHuqA87+HT5gJjrWQ8YI3/v/XLiwKismNWS/PAohhBBiEAvrElCl1J+VUiVKqX1+zi9SSlUppXY1vf49VH1rHfpXd/3qV79iwoQJrFixgnvvvRen0wl4A8PmfXUvv/wy8+fPJzY2lqysLF5//fWm59Ats4ZLlizhj3/8IwBut5vq6mpiYmKoqalp6Wvp0qX8+c9/pra2FoBTp05RUlLCJZdcwltvvUVDQwM1NTW89957Psc6d+5cXnnlFQBeeukl5s+fD8Do0aPZvn07AO+8807LM7TvH+Dvf/875eXlNDQ08PbbbzNv3jyGDRtGSUkJZWVl2O123n///Zb2vu4hRHta6+D3/3VW/09L/T8hhBBCDF7h/hX388DvgBc6afO51vrqvhlO72reA9hs2bJl3Hvvvfzv//4vW7ZsISYmhksuuYQnnniCn/zkJ0RFRbF//34uvvhi4uLiePXVVwFv4PXNb36TJ554AqfTya233kpeXh7/8z//wwMPPMBzzz2H0Wjkj3/8I3PmzGHevHlMmjSJ5cuX89RTT3HgwAHmzJkDeJO1vPjii0yfPp1bbrmFqVOnMmrUKBYsWODzGX7zm99w77338tRTT5GSksJf/vIXAO6//36uu+46Zs6cyZIlS4iKigJgypQpmEwm8vLyuOeee0hISGD+/Pl85Stf4ciRI9x+++3k5+cD8O///u/MmjWLrKwscnNzW/q85557+MY3voHNZmPjxo2yD1D4ZNd23NqN0WDstN3mtVYuv9Z//T8PHqKMUaEenhBCCCFEv6B0T6auQjEApUYD72utJ/k4twj4flcDwPz8fN0+sciBAweYMGFC9wcaBtHR0S0zdYPF888/z7Zt2/jd734X7qEENBA/ZoayMlcZp9yniFbRftt4PDAzcxTvbSkmPdP3EtBaTy25EbkBZxJF/6CU2q61zg/3OAYKX98fhRBCDE7+vkcOhCygc5RSu5VSHyqlLgr3YIQQ/VOlpxIz5k7bHP7CTGy8x2/w59ZuTMoU8D5CCCGEEANVuJeABrIDGKW1rlVKXQm8DYzz1VAp9QDwAMDIkSP7bIC9abDN/oF3Oec999wT7mGIQcat3dR56ohSnS/d3LTGxqwA+/+ijdHdSogkhBBCCDEQ9OsZQK11tda6tunvHwBmpVSyn7bPaq3ztdb5KSkpfTpOIUR4NWhvUBcocNu81sbsTur/uXBJAhghhBBCDGr9OgBUSqWppp/olFIz8Y7Xd/EuIcSQVeOuwRDgy5m3/p+VmQv8zwAC2AySZEgIIYQQg1dYl4AqpVYAi4BkpVQx8GPwbr7RWj8N3AR8UynlAhqAW3W4s9YIIfqdYMo/BNr/59EeFEoKwAshhBBiUAtrAKi1vi3A+d/hLRMhhBA+ObQDh3YQbfCf/RNg4+oA+/9wEm2Q/X9CCCGEGNz69RLQwaKsrIypU6cydepU0tLSGD58eMt7h8PR6bXbtm3jO9/5Trf7fv7553nwwQc7bbN69Wo2bNjQ7T6ECKc6d11Q7TavtTEnUAF4g+z/E0IIIcTg1t+zgA4KSUlJ7Nq1C4DHH3+c6Ohovv/977ecd7lcmEy+/yvy8/NbCqX3ltWrVxMdHc3cuXN7tR8hekONpwZTgC9lzfv/fvyr8522k/1/QgghhBjsZAYwTO655x4efvhhFi9ezA9+8AO2bNnC3LlzmTZtGnPnzuXgwYOANzi7+uqrAW/weO+997Jo0SLGjBnDb37zG5/3/stf/kJOTg4LFy5k/fr1Lcffe+89Zs2axbRp07jssss4d+4cx48f5+mnn+ZXv/oVU6dO5fPPP/fZToj+yKM9VHuqA+7/O7TfQnyim7Thvvf/NW8ttipryMcohBBCCNGfyAxgZzZuhNWrYdEimDMn5Lc/dOgQn376KUajkerqatauXYvJZOLTTz/lRz/6EW+88UaHawoKCli1ahU1NTWMHz+eb37zm5jNF4pWnzlzhh//+Mds376duLg4Fi9ezLRp0wCYP38+mzZtQinF//7v//Lkk0/yi1/8gm984xttZiUrKip8thOiv2nUjXjwYFCd/y5r0xorswKUf7AZbBiVMdRDFEIIIYToVyQA9GfjRliyBBwOsFjgH/8IeRB48803YzR6f+Csqqri7rvv5vDhwyilcDqdPq+56qqriIiIICIigtTUVM6dO0dmZmbL+c2bN7No0SKaayHecsstHDp0CIDi4mJuueUWzpw5g8PhICsry2cfwbYTItxqPbVBtdu81sbyG/y3dWonyUafJUaFEEIIIQYVWQLqz+rV3uDP7fb+uXp1yLuIiopq+fu//du/sXjxYvbt28d7771HY6Pv2YqIiAsp6o1GIy6Xq0Mbf1kMv/3tb/Pggw+yd+9ennnmGb99BNtOiHCr8lQFLNvQvP+vsxlADx6iDFF+zwshhBBCDBYSAPqzaJF35s9o9P65aFGvdldVVcXw4cMBb+bO7po1axarV6+mrKwMp9PJ66+/7rOPv/71ry3HY2JiqKmpCdhOiP7EpV3Ue+oDJoA5uM9CQpKbYRm+9/8BaLTs/xNCCCHEkCABoD9z5niXff7nf/bK8s/2/uVf/oUf/vCHzJs3D7fb/w+qgaSnp/P4448zZ84cLrvsMqZPn95y7vHHH+fmm29mwYIFJCdfWO52zTXX8NZbb7UkgfHXToj+pF7Xo1AB6/YF2v/n1m4syoJZmf22EUIIIYQYLFRz9rvBJD8/X2/btq3NsQMHDjBhwoQwjUgMRPIx07+dcp6i0l0ZsHTDN24expU31XLtLb7rBTZ4GogzxpFpzvR5XvRvSqntWuverZUziPj6/iiEEGJw8vc9UmYAhRADjtaaSk9lwPIPHg9sXWdl1oJOZgBxE6Vk/58QQgghhgYJAIUQA45d23Frd8CyDcHs/wMpAC+EEEKIoUMCQCHEgFPvqYfOt/4Bgff/ebQHhQqYSVQIIYQQYrCQAFAIMeBUeaowEzhpy6Y1NmYvavB73omTaEN0wEQyQoSDUmqZUuqgUuqIUupRH+fjlFLvKaV2K6X2K6W+Go5xCiGEGFgkABRCDChu7abWU4uFnu//c+EixhAT6iEK0WNKKSPwe2A5MBG4TSk1sV2zbwFfaK3zgEXAL5QKsDFWCCHEkCcBoBCiV3i0B6d2hvy+DboBjQ44a1ew10JSipvU9M7r/8n+P9FPzQSOaK2Paq0dwCvAde3aaCBGeT8ZooFywNW3wxRCCDHQSADYx9566y2UUhQUFLQcO378OJMmTerW/SorK/nDH/7QrWvnzp3brev6QleeK5jn+PWvf019fX1PhyW6oMRdwlHHUdy6+3Utfan11GII4kvX5gD7/7TWoJEC8KK/Gg4UtXpf3HSstd8BE4DTwF7gn7XWnvY3Uko9oJTappTaVlpa2lvjFUIIMUCYwj2AcDnsOEyDx//eoK6yGWyMs4wL2G7FihXMnz+fV155hccff7zH/TYHSv/0T/8U9DVutxuj0ciGDRt63H9vcLvdXXquYJ7j17/+NXfeeSeRkZGhGKIIwK7tlLhK0GjK3GWkmlJDdu9Kd+DyDwCb1tq4+su1fs+7cGEz2AJmEhUiTHxNcbcv3LsU2AVcCowF/q6U+lxrXd3mIq2fBZ4Fbx3A0A9VCCHEQDJkZwAbPA1EG6JD9gommKytrWX9+vU899xzvPLKKz7buN1uHnnkEWbMmMGUKVN45plnWq5dsmQJ06dPZ/LkybzzzjsAPProoxQWFjJ16lQeeeQRtNY88sgjTJo0icmTJ/Pqq68CsHr1ahYvXsztt9/O5MmTAYiOjm7p98knn2Ty5Mnk5eXx6KMdcg1wzz33sHLlypb3zdeuXr2aRYsWcdNNN5Gbm8sdd9zhnVkBtm7dyty5c8nLy2PmzJnU1NT4fb7242v/XP6eP5ix/OY3v+H06dMsXryYxYsX89xzz/HQQw+1XP+nP/2Jhx9+OOD/nwjeGdcZDBiIUlGcdZ3Fru0hua9DO3BoBybV+e+ugtn/59RO2f8n+rNiYESr95l4Z/pa+yrwpvY6AhwDcvtofEIIIQaoITsDGA5vv/02y5YtIycnh8TERHbs2MH06dPbtHnuueeIi4tj69at2O125s2bxxVXXMGIESN46623iI2N5fz588yePZtrr72Wn/3sZ+zbt49du3YB8MYbb7Br1y52797N+fPnmTFjBpdccgkAW7ZsYd++fWRlZbXp88MPP+Ttt99m8+bNREZGUl5e3qXn2rlzJ/v37ycjI4N58+axfv16Zs6cyS233MKrr77KjBkzqK6uxmaz+X2+9uM7fvx4m+dyuVw+n7/9PjBfY/nOd77DL3/5S1atWkVycjJ1dXVMmTKFJ598ErPZzF/+8peWQFT0nF3bqXJXEa282TUN2sB513mGm9uvXuu6OnddUO0OvHuaJGscqdX7Id33z8MePEQZpAC86Le2AuOUUlnAKeBW4PZ2bU4CS4DPlVLDgPHA0T4dpRBCiAFHAsA+tGLFCr773e8CcOutt7JixYoOAeAnn3zCnj17WmbbqqqqOHz4MJmZmfzoRz9i7dq1GAwGTp06xblz5zr0sW7dOm677TaMRiPDhg1j4cKFbN26ldjYWGbOnNkh+AP49NNP+epXv9qyPDIxMbFLzzVz5kwyMzMBmDp1KsePHycuLo709HRmzJgBQGxsbKfPZ7FY/I4PvPu1fD1/WlpawLHMnz+/TZuoqCguvfRS3n//fSZMmIDT6WyZFRU9V++uR6FagnOrslLuKWeYHhZw5i6QGk8NpkBftg4WsPk/DjDbdBoe+xk88QSM9x0Eyv4/0V9prV1KqQeBjwEj8Get9X6l1Deazj8N/CfwvFJqL94loz/QWp8P26CFEEIMCBIA9pGysjI+++wz9u3bh1IKt9uNUoonn3yyTTutNb/97W9ZunRpm+PPP/88paWlbN++HbPZzOjRo2ls7Li8rXn5pS9RUb5nO7QOnFHRZDLh8Xha2jscjpZzEREXimgbjUZcLpffe/p7vtWrV/sdH8BLL70U1PP7Gosv9913Hz/96U/Jzc3lq1+V0lmhVOWpwqwu1OgzKAPao6l0V5JsSu72fT3aQ7WnOnDQtncfm0tncE3a38Dpgr37OgSALu3CrMxtxilEf6O1/gD4oN2xp1v9/TRwRV+PSwghxMA2ZPcA9rWVK1dy1113ceLECY4fP05RURFZWVmsW7euTbulS5fyxz/+EafTmz7/0KFD1NXVUVVVRWpqKmazmVWrVnHixAkAYmJiqKmpabn+kksu4dVXX8XtdlNaWsratWuZOXNmp2O74oor+POf/9ySJdPXEtDRo0ezfft2AN55552W8fmTm5vL6dOn2bp1KwA1NTW4XC6/z9de++fy9/zBan+/WbNmUVRUxMsvv8xtt93WpXsJ/9zaTY2npkONPquyUuouxdMxQWHQGnUjHjwYVOdfttwTJ7Gl4mJmJW8Hswkmd8ywK/v/hBBCCDFUyQxgH1mxYkWH5Co33ngjL7/8Mj/4wQ9ajt13330cP36c6dOno7UmJSWFt99+mzvuuINrrrmG/Px8pk6dSm6ud0YjKSmJefPmMWnSJJYvX86TTz7Jxo0bycvLa5lhTEtLa1N2or1ly5axa9cu8vPzsVgsXHnllfz0pz9t0+b+++/nuuuuY+bMmSxZsqTT2ToAi8XCq6++yre//W0aGhqw2Wx8+umnfp+vvfbP9YMf/MDn8wfrgQceYPny5aSnp7Nq1SoAvvzlL7Nr1y4SEhK6dC/hX6Nu9Fmjz6RMNHgaqPXUEmuM7da9az3+M3q2VuCYQkqmgZSvLfcGfz6Wf7pxE62ifVwthBBCCDG4qc6WDA5U+fn5etu2bW2OHThwgAkTJrS8D1cZCNF/XH311Tz00EMsWbLE5/n2HzMisLOus5x3nSfS0LHchl3bMSsz2Zbsbt37sOMwHu0JuGzzz/8Tx7HDZv7zd/63QtV6asmx5GA1yB7AgU4ptV1rnR/ucQwUvr4/CiGEGJz8fY8csjOAEqwNXZWVlcycOZO8vDy/wZ/onmpPtd8afREqglpPLQ2eBmwGW5fu69Iu6j31Qc3abV5r5Zpb/c8WerQHAwYiVITfNkIIIYQQg1VY9wAqpf6slCpRSu3zc14ppX6jlDqilNqjlJruq50QXREfH8+hQ4d4/fXXwz2UQUVrjd1jx0i7wuoHC2DlSjhYgAED591dT1JY72mbWdQftxu2rLMy+5JO6v/hJNoQHfBeQgghhBCDUbiTwDwPLOvk/HJgXNPrAeCPfTAmIUQ3uHF33P93sAAeewxefBEeewzb4RNUeCpw6s6TCLVX7anuGFj6cGCPhdQ0N8nD3H7buHARbZD9f0IIIYQYmsIaAGqt1wKdVR2/DnhBe20C4pVS6T3or7uXiiFGPla6zqmd3kpkre3d5y3F4PGA04Xaux+ACndF0PfVWlPlqfK7tLS1zWtszLqk8729Gt3lJahCCCGEEINFuGcAAxkOFLV6X9x0rMusVitlZWXyg70ISGtNWVkZVqskCOkKJ86On1+TJ3lLMRgMLSUZbNgodZfi1v5n6Vqzaztu7caoAs8Abl5rZdZC/8s/tdagpQC8EEIIIYau/p4ExtcmHZ8RnFLqAbzLRBk5cmSH85mZmRQXF1NaWhrSAYrByWq1kpmZGe5hDChOjxPV/lN2fC488YR3JrCpJIMRcHlcVLurSTAFLsFR76n3/ZWgHbcbtq638tM/+t9j6MKFzWALKpgUQgghhBiM+nsAWAyMaPU+Ezjtq6HW+lngWfCmuW5/3mw2k5WV1RtjFELgrQHoc5/e+NwOtfisykqJp4R4HR8wGUuFp6JDYXlfgtn/59AOUowpAe8lhBBCCDFY9fcloO8CdzVlA50NVGmtz4R7UEKIjhp0AyYV3O+UzMpMo6eROl3XaTu3dlPnqcNM57X/ADattjF7YeD9f1GGqKDGKIQQQggxGIV1BlAptQJYBCQrpYqBH4P3Jz2t9dPAB8CVwBGgHvhqeEYqhAjEru1EEHxtPTNmSl2lRFv8Z+Rs0N6ALpiSDZvXWrn+Tv/1/5rJ/j8hhBBCDGVhDQC11rcFOK+Bb/XRcIQQ3eTWbty4MajgFxVEqAiqPdU0ehqxGnwHZTXuGgxBLFRo3v/3/57xv8fXpV2YlRmzCjybKIQQQggxWPX3JaBCiAHApV1+0jP5p5TCiJEyd5nfNpWeyqDKP3yx20JahpvkVI/fNk7tJMYQ07VBBlBRUcHJkydDek8hhBBCiN4kAaAQosecdK2wezObslHmKfNZGN6u7Ti1M6h9hcHU/3PjJlqFtgD8uXPnWLlyJZs3bw7pfYUQQggheosEgEKIHnPu2AIffQQHC7p0XfPevnJ3eYdz9dvXw8fB3TNQ/b9m/paadkdhYSE5OTncfffdrFmzhsbGwP0LIYQQQoSbBIBCiJ7ZuBH7gw9gePNteOyxLgeBPgvDb9xI1WPfxfTKGwHv2bz/b+YC/zOAHu1BoYhQwSep6UxdXR2vv/46LpeLpKQk5s+fT319fUjuLYQQQgjRmyQAFEL0zOrVOC0GDHYnOF3eou9dYFRG3NpNtbu65ZhnzWpqh0VjqaoPeM/9uyykDQ+w/w8n0YbooLKJBmP//v3k5ORgsXj3J86dO5eEhMBF7YUQQgghwk0CQCFEzyxahCMhGoNbg9kEkyd1+RY2ZeOs+yzexL/QeOk83BEWDKiA99y8xsbsAPv/XLhCmgDm6NGj5OTktLz3eDz88pe/xG63h6wPIYQQQojeENYyEEKIQWDOHJz/9RMM+w7ARZNgfG6Xb2FSJho8DdR4aog1xlI7PRf13e/CrkPe4K+Te25ea+XGuzqv/6fR2Ay2Lo/LnwULFpCYmNjy3mAwkJSUxMmTJxk3blzI+hFCCCGECDUJAIUQPebMHk3kuInQgyWWESqCs+6zRBmiqPJUETF2AmRP6fQalwu2bbDys2f91//TWoMOXQH4+vp6oqOjsdnaBpRZWVkcO3ZMAkAhhBBC9GuyBFQI0SNu7UYr3eP9dRZloVE3UuQqosHTgCmI3099sTvw/j8XLmwGG0Zl7NH4mu3du5e1a9d2OD527FiioqJC0ocQQgghRG+RGUAhRI+4cXuLwIcgv0oUUVS6K1GooALK5v1/Wms2fLaBstIyll6/lIiIC9k+ndpJsjG554NrcubMGUaMGNHheGZmJpmZmSHrRwghhBCiN8gMoBCiR1za1TFYO1gAK1d2qy5gjIoJumD7pjU2Zi9qZP+u/Zw8dpL8ufltgj8ADx6iDKGbmTt79ixpaWk+z7355puUlvpfjiqEEEIIEW4SAAohesSNuyV7J+AN+h57DF58sVt1AZUKbvavef/fjPkNFOwp4JLLLyFjZAZ7tu2h5ExJSzuNDtn+P4Dp06eTmprq85zWmuLi4pD1JYQQQggRahIACiF6xK3dbZd/7t0HThc1DhvFValdrgsYrC92RZAxwkVSiofr77yejJEZADTUN7B/5/6WsVmUBbMyh6RPj8fDjBkzMJt93y89PZ2zZ8+GpC8hhBBCiN4gAaAQokec2onSrSLAyZM4bs/ixk0ruHf7H9GTul4XsFNNy0s3raxm1iUNFOwtoORMScus4fhJ4zlScAStNQ7tCGn9vz179vDuu+/6PZ+WlobT6QxZf0IIIYQQoSYBoBCiR5zaiaHVl5KyxIncsvs17vnyEYxpyWw4PTV0nbVaXrr5pfPMzi5k5+adeNwXsoDGJ8ZjibBQVVGFGzdRKnT7/86dO0dysv+EMmPGjOHaa68NWX9CCCGEEKEmAaAQokfs2o5BXfhS8tpfYrn0Wju3P53NV77byP/9MS50nTUtL3W5FNvKp5JnXk1FWQVpmW2Tsnzlm18hPjEeIKQF4MvKykhKSuq0zapVq6ivrw9Zn0IIIYQQoSQBoBCiR5w4MeKtsedywUvPxnLnN6oBuO62Wraus3LqRIgqzkyeBGYT+2svYrjtLM7sOFLTUjEa29b4q6mqYe/OvSgUESrCz826LiUlxW8CmGZHjx6lpKSk0zZCCCGEEOEiAaAQokdaLwH9x/uRZIxwcdFUBzXVNURFa665pZY3ftXYrbIQHYzPhSeeYNOoB5h1jZkRly7imluv6dDM7Xaz6fNNRBuie1ygvrXLL7+cxMTETtukpqZKACiEEEKIfksCQCFEt3m0B7d2tywBXfGnWO78ehUAaz5ew55te7hq5hd89KLqdlmIDsbnsrliJrOvs3Kk4Ahul7tDk4SkBOob6lH1oQv+qqurWblyZcB2EgAKIYQQoj+TAFAI0W1u3KimGhAeD+zcbMVg/ITDBw4z79J5bFy9kYmeVZTZEzhWkwkOJ3y2qkd9ulywfaOVGfMbWf3halxOV4c2SilSh6dSebayR321VlZWRk1NTcB206ZN44orrghZv0IIIYQQoSQBoBCi29zajcZbBP7kURMx8W6Kj+8lY0QGCUkJjBo7iiNWG5enreLjc5eD1vDppz2aBdy/M4LhI51YbbW43W5i4jqWedBac+k1lzJh7IRu99NeeXl5wOWfAEajkcLCwpD1K4QQQggRShIACiG6zc2F5ZcFeyMYmVVO2vA0oqK9pRdmzJ/ByMWXsOyqCj4uuazpInePisNvWmNl1iWNlJWUkZic6HOPnwsX0ZZozp051+1+2mtoaOi0BEQzpRRvvPEGDocjZH0LIYQQQoSKBIBCiG5z6QvLL7/YbWFMTg0Tp05sOZaU4i2ZMO3uNE7Wj+C0PQPMJm82z27avNbG7IUNpKSlsHj5Yp9tnNoJtfDee+91u5/25s+fz7x58wK2MxgMJCYmUl5eHrK+hRBCCCFCRQJAIUS3ObWzZQ9gwR4L8y+LIWdizoUGBwtY859PcebsaZZcWcvHmT+AJ57wZvPsTn9O7/6/mQsaaWxoJC7Rd41BDx6GpwynoqICl6vjHsHu2LRpU9D1/SQAFEIIIUR/JQGgEKLbHNrRUgJi/y4zp4s+uHDyYAE89hiZO7dS9P+eYtllZ/no2NxuB3/g3f+XOcpJQpKHT9/7lLPFZ/22jTZHk5CQwPnz57vdXzOtNZ999lnQJSUWLFhARkZGj/sVQgghhAi1sAaASqllSqmDSqkjSqlHfZxfpJSqUkrtanr9ezjGKYTwza7tGJSBynIDVZWKlLTaCyf37gOniwyLkbO1dubFrOHgPgulZ43+bxjA5rXe/X9aa8pKy0hKTerQxq3dmJUZi7KwbNkyoqOju91fs/r6eoxGIzabLaj26enpWCyWHvcrhBBCCBFqYQsAlVJG4PfAcmAicJtSaqKPpp9rrac2vf6jTwcpxCCwZcsW3nzzTaqrq0N+bydOjBg5sMdC5shy0ocPu3By8iQwm0ixRTA5KZqI6RNYtKyBT96J7HZ/m9bYmLWwgfo671LMyKiO93JqJ1EGbxKarKwsTCZTt/trFmwG0GZFRUWsWLGix/0KIYQQQoRaOGcAZwJHtNZHtdYO4BXgujCOR4hB5/Dhw2zcuJHIyEi++OKLkN/f4fEuAS3YY2H4qDJS01MvnByfC088gfmur3DRb3+Ba2w2y66v46OXFKxc2eVSEE4n7NhoZeb8RpRSzL10rt8MoDHKWxriwIEDvPPOOz16RoC0tDRuuummoNsnJSVRVlbW436FEEIIIUKt578a777hQFGr98XALB/t5iildgOnge9rrff3xeCEGAxiYmK46aabGD58eMjv7dZuPMqDQRk4UmBh8fJURo6xtm00PhfG57Lqb5+RvP8wlxSV8IPtP6Tiz++REPVKlxLC7N8ZQeZo7/4/rW1Mnj7Zb1ubwbtUMykpKSR7AKuqqoiIiAi6fVRUFC6Xi4aGhqCXjQohhBBC9IVwzgD6yqag273fAYzSWucBvwXe9nszpR5QSm1TSm0rLS0N3SiFGKDq6+uJiYlpCf4OHDjAhx9+GLL7u3C1fMYeO6Koq93jt21SQw0lv/4tkaveY17iJj49uwicri7VA9y0xsrshY0AbF67mW0btnVoo7VGobAo7/67xMREKioq8Hg8wT+YD2vXru1ScXelFPPmzcPtdgduLIQQQgjRh8IZABYDI1q9z8Q7y9dCa12tta5t+vsHgFkp5bMSs9b6Wa11vtY6PyUlpbfGLMSAsWvXLlatWtXyPiMjgz179vQ4GGrm1u6WX+OcLDRiNJ7w2za5tISyejtozbJhf+ejksu7XA9w0xobsy5pAKCqosr3/j+cRBuiMSjvlzaLxcKMGTNwOp1deLKOuroHEGDhwoUhSUAjhBBCCBFK4QwAtwLjlFJZSikLcCvwbusGSqk01bTJRyk1E+94ZWONEEEoLCwkOzu75X1cXBzR0dGcPeu/dEJXuHChtcblgtJzEYyb6D/rZdLcmQyLigCDgcUZG9hWPZOaH/ws6OWfTifs3OSt/wdQWV5JfEJ8h3YO7SDGENPm2NKlS7u0fNOX8vJyEhISunTNtm3bWL9+fY/6FUIIIYQItbAFgFprF/Ag8DFwAHhNa71fKfUNpdQ3mprdBOxr2gP4G+BWrXX7ZaJCiHbcbjdFRUWMHj26zfG8vDwaGhpC0ofL4y2wfvqkidi4elLSfBdlB7Dm5bHoT7+FO+8k5qkfMeNSN58dnhp0X/t2RDAiy0l8onf2Mj4x3m8R+Ob9f83Wr1/Pzp07g+6rPa01ixYt6vJsnsVi4cyZM93uV4hApZKa2ixqKpO0Xym1pq/HKIQQYuAJZxKY5mWdH7Q79nSrv/8O+F1fj0uIgc7tdrN06VKs1rZJWebPnx+yPhw4MGKk6JiZcRON5FyU02n7tSdKyLp4FiOyRrDs+jo+fjuK626r7fSaZs31/5ot/dLSDm201qAgQrWd7TMajZw5c4Zp06YF1Zev+86YMSPoIvDNupsJtKSkBKUUspR9aGtVKulyvFsmtiql3tVaf9GqTTzwB2CZ1vqkUirV582EEEKIVsJaCF4I0TsMBgMXX3xxh+N2u52XX36ZUEykOzwOjMrIyWMmYuPLMBg6/3Li8XgoOVsCwJKr61n/mY36uuCCqtb7/yrKKvj87593aOPGjVVZMam2v9fqaUmGAwcO8Prrr3f5usTERMxmc5ev27lzJ4cPH+7ydWLQCaZU0u3Am1rrkwBa65I+HqMQQogBSAJAIfqIw+Hgiy++oKamhoMHD/ZqX++//z67du3qcNxisXD69OmQFIV34K0BePyIor52b8AZsqTUJMpKvIFYQpKHvPxG1n4SuCh8+/1/ZSVlVJRXdByPdrTU/2stOTk5YHDamYqKCuLj47t8nc1m49577+3ydd3Zbyj6N6VU1zIIefkqldS+nksOkKCUWq2U2q6Uuqu7YxRCCDF0SAAoRB/ZsGEDBw4cwOFw8Pbbb9PY2Bj4om46deoUaWlpHY4rpRg+fDinTp3qcR9O7cSAgaOHFOkjGgMGgMmpyW3KIiy7vo6P3ooK2M/e7RGMHHNh/19lhe8EMG7cRBk63i8hIYE77rgjYD/+dCcDaLNNmzZx7ty5PutP9FublVKvK6WuVMGvJQ6mVJIJuBi4ClgK/JtSqsNabCmTJIQQojUJAIXoAx6Ph23btrFw4UKSkpLIzs7uUWKSzrhcLioqKvzuIRsxYgRVVVU96kNr3RIAFh01kTnaEfCa9Mx0lt+wvOX95dfWs/ojG3Z759dtXmtrs/+vrqaOuISOCWAUCqvB2uE4wLp166io6DhrGIzExETS09O7de3Zs2e7HGxfeumlEgAOPjnAs8BXgCNKqZ/6CtTaCVgqqanNR1rrOq31eWAtkNf+RlImSQghRGsSAArRB44fP05cXBzJyd4yllOnTqWgoKBX+rLb7eTn52M0Gn2enz9/PnPmzOlRHy68GUCVUpw7E8Xl14wN6rqNqzfS2OAN5lLS3Iyf5GD9p50vA928xtqy/w9g4dKFTMmf0qaNW7sxKiNmfO+5O3nyZLfLX8yfP5/hw9uvvAtOV/cfut1uxowZ0629g6L/0l5/11rfBtwH3A1sUUqtUUr5+2QMWCoJeAdYoJQyKaUigVl4s2oLIYQQfkkAKEQfyMrKarMMsf37UIqKimLZsmV+zzscDtas6Vm2eKd2opSiqsKAy6nInhAf1HUnCk9QUXZhJm7Zl+r46G3/y0AdDti52cqM+RdmAPds39OhsLtTO4lRMX6XoXY3EYzL5eL//u//up00p6v9FhUV8dJLL3WrL9F/KaWSlFL/rJTaBnwf+DaQDHwPeNnXNcGUStJaHwA+AvYAW4D/1Vrv6/UHEkIIMaBJAChEH9i7dy8m04XslAaDgTNnzoRkL157GzZsYM+ePX7Pm0wm1q1bhz3Q2stOuLS3CHzRcRNxCWWcPhncc8QnxlNZXtnyfumX6vjH+5G0i+da7NkWwaixF/b/ud1u1ny8psPspku5OhSAb627AWBFRQWVlZVdLgHRLCcnhxtvvDHo9rL/b9DaCMQCX9JaX6W1flNr7dJabwOe9neR1voDrXWO1nqs1vq/mo493a5c0lNa64la60la61/39oMIIYQY+CQAFENeKEoidHbvY9XHePO9NzsELadOnfKZqbOnTpw40ekSQoPBQEpKCj1JBuHU3ojt5FEzMXHniU+MD+q6+MT4NjOAGSPdjBzjZPMam8/2G1fbmL3owvLPmqoaoqOjO/xbKu1//x/AlClTuPLKK4MaY2s9DchMJhMHDhzA4/H0SX+i33pMa/2fWuvi5gNKqZsBtNb/Hb5hCSGEGIokABRDWr2nnmPOY70WBDbqRvac2IMpzUSJpwS3vpAFc+TIkRQVFXVydfeUlJQELCKekpJCSUn3S4bZtR0jRo4eMhITd5bo2Oigrps2axr58/LbHPOZDfRgAaxcyaYPPMxZeCEArKqoIjYhtk3T5v+79gXgWzOZTBw6dCioMbZWX1/fsm+zuz799NOgk+6kpKQwatSoHvUn+qVHfRz7YZ+PQgghhMCbQlqIIamgoICth7cyargiaf1rxOUvhB4mR2mv3F1O+dlyRqSPoNRdSrWnmhHmEUQaIklPT6e8vBy73U5EhP/gpSvcbjdGozHgLNIVV1yBxWLpdj+NuhGjMnLssImpM6OCrrNnMBooPl5M1rislmNLv1THLZdm8JPfgNGIN/h77DHsjQb27HiQ/GHrgGwAhmUMY+HShW3u6cRJpCESg/I/BqUUb7/9NtnZ2V36t542bVrQbf1JSkoKurZfXl6HBI5iAFNKLQeuBIYrpX7T6lQsNGVSEkIIIfqYzACKIamhoYG/f/p3yo9/weffepwzq19DX3YZbNwYsj5c2kX54W1MPXmSqfGRRBui8eDhsOMwZ5xnwAD3339/m72BPWU0GnnwwQcDBmRGo7FH+w+bZwCLjlm59MoRbc5prWn0NNLoaWwz4wngcXv48M0P28y4js52kZzqZvuGpiWce/eB08WO8snkRB8h5tiuC/022omJbbvXz6mdne7/A28A2J19gDt27OhxyYxg+9Va8+yzz3ZIcCMGtNPANqAR2N7q9S7eun1CCCFEn5MAUAxJNpuNu755F5dkxjFBQX2sjZpkG6xeHbI+aravRf/6VzS+9ApRP/spHCwgQkUQpaIodZdyxHkEt9nd7fp0vpw+fZrdu3cHbFdXV8fbb7/drT5a1wA8cgCqK7a3vTd1RBgiiDZGU6/r25yLsEZgMpmoraltc7zNMtDJk8BsYmPFbOakbvO+b/L5p59z8tjJtuNBE2novJQEdC8RzLp163A4Atc47MzMmTPJzs4O2K6uro7KykopATGIaK13a63/CmRrrf/a6vWm1jp0n/hCCCFEF0gAKIacuro6XnnlFSpcFUTkTCQvOQZ7vYPaEUmwaFHI+qkq2IqnvJY3isvB6fLObAEGZfDOBmoP/9j/D95f+36HmbLuOnHiBKdPt68V3VF8fDy1tbW4XF1fhdZcA7C2xkBDvZHktAsBUqOnEauyMto8mhGmEZiUqcOzJSQlUFXedlZt6fV1fPxOFFoD43PhiSfYZLyK2d+f5H3fpKq8irj4tkXgNRqr8p8Aptm8efMYMWJEwHbNPB4PVVVVQS3d7ExycnJQs7zBLhMVA9JMpdTflVKHlFJHlVLHlFJHwz0oIYQQQ5MEgGLIOXToEBigmmoisi+i/l8fY6UxmZrf/jykewDrpk2gssZOcoQZg8XcZiYLvElLRg4bydEzRzniPEK9p97PnYJXUVERVBBhNBqJj4+nvLy8y324tAsUHD9iJim1koRWGUCdOBlpGolRGVFKkWhIxK7blpuYs2gO8UnxbY6Nm+AkMtLDnm3e/Xl1wydw4FQGF3/5QjIbrTVVlVXEJVwIAF3aRYQhApMKHGClpaV1aXatqqqK6OjoHi/Rraio4C9/+UvAdo2NjV0KUMWA8hzwS2A+MAPIb/pTCCGE6HMSAIohp7CwkPSsdNDevWFR06YRN3cORdG2kGUDdWon7rGjKb/rqyQvvRyeeKLNTFazlLQU6srqcLldHHYc5qzrLB4dXMkAX7pSRmDZsmVERfkvwu6PEydobwCYmlbVEsw5tRObwdamHEOsMRa3ajsDmDEyo0NQpZR3FrB5Gej2DVYummbHFnnh/8Pj8TBz/kwirBeSuDi1k1jVNiuoP6dOneLll33W3PYpNjaWu+66K+j2/sTHx1NTUxNwtjUnJ4dly5b1uD/RL1VprT/UWpdorcuaX+EelBBCiKFJAkAx5NTW1hI3Og6LsnDssImnHktgVNYoThw70bK8sacc2rssMnX2THK/8TWfwR+AxWLh0isvxazNRKkoSlwlHHYe7vZs4A033EBWVlbghsCYMWO6Nbvl8nj/jY4fMTNnURIJSd4ZR7u2E2+Ib9PWpmyYMLUJagsPFvLJu590uO+VN9bx3mvROJ3e+n9zFjW2OW80GjuUkHDjJsoQXBDbvAcw2CC/qqoqJAl6jEYjCQkJAfcfbtiwoVszsmJAWKWUekopNUcpNb35Fe5BCSGEGJokABRDzm1334YhxoAZMy/8IY6nn0rA7b6YlPSUlsCtpxo9jaAgbXg6b7w4kYK9/ksujJ80Hq11m72Bhx2HOec616XZQI/HQ1FRUdDLHHfu3MlHH30U9P2bNepGjBg5srkG5/53vWUbmkQb2tYDNCgD8YZ4GvWFYC4hMYHKssoO952Y52D0WCfvvBzNpjVWZreq/wdQsLeAz/72WYfrOisA31pkZCRKKerrgwuut2zZwv79+4NqG8js2bM7FK9vb/PmzSHpS/RLs/Au+/wp8Ium18/DOiIhhBBDlgSAol/QWvdaMfbWjh49ysYdG0GBw27gvVejuf/hSl56JouR2SOxu+2BbxKEOl2HSZv42aOreOH3MXxlWTo///cE7I2qQ9tNazaxfcOFTJrNmULPuc51aW9gdXU1f/vb34IeY3eyYoJ3ps9QeJSjGyqwFLwLjz2G5+ABDBiwKVuH9jHGGDxcCGTjEuOorqrG4+kY3D74owp++18JFBZYmDqr7QxgZXkl1sgLwZ5HezBgwELw9Qznzp3rs19fysrKSEpKCvrenbn44os7LShvt9upr68nPj4+JP2J/kVrvdjH69Jwj0sIIcTQJAGgCDu3280LL7wQVPbKnjp06BBnas4QQQSfvBvJxDw7D/24gi92R/C7f9vI6bLQjKHOU4dBG1j/2TQe+F4Ff9tWzLFDZq7KH87mtW1nrBKSEqgsr2xzrHk20K3dQc8GBpsApllzgfKusms7xr0HKKofyZjIE+B0YT+0n1hjLEp1DHDbB4Vms5m8/Dyf9e5mXdJIWqaLvBmNtK/X3j4BjBMn0YZon336s2DBAmJiOq8Z2CyUAeCJEyd4/fXX/Z4/f/48SUlJAes3ioFFKXVn058P+3qFe3xCCCGGJvlpQ4Tdrl27AEhPT+fVV1+lrq6u1/o6XnScuPQ4zIcKef2/G7h56UEirJrb7q/myP7ZHD91vMd9uLUbJ06Kjjg5fiiXLyetILV6P79/pYRH/quch+9J5V//KZnqSu+nX0JSAuXnfQdi7WcDGzwNPttB1xLAAERHR5Obmxv0jBh4Z2od2kFN5lSc2sKIyAowm3BPyCHOEOfzGrMyYzVYvdlDmyy4fAER7SM8vMlg/vN35/nnf+tYIi0yMpLk1AuzaE4CF4Bvb8eOHXz++edBtZ03b17IZuRiY2MpKiryez4jI4O77747JH2JfqV5g2qMn5cQQgjR5yQAFGGltWbDhg0sXrwYg8FAREQEe/bs6bW+TpWeIqW+juKHf88XB+O4Yu034WABk6bZKS9N52TxyR4vRW0ue/Dm/2hmx71L3FvPwWOPwcECll5Xz4c7ilEKlk3L5ON3IklITiA9M93v/VrPBh5yHPI7Gzhy5Ejy8/N93ME3pRRXX311l2admpPkFDovYvxEJ1O/dZ83w+mYMZ3uxYs1xLYpB7Ftwzb27dzns23ORCf58zouxV1w+QKGZQxrc8xm6LjktDMRERGcOXMmYDuPx8O0adNCkgQGvJlA7XY7DQ2+A/gTJ070uOC86H+01s80/fkTX69wj08IIcTQJAGgCCu3201eXl5L/bOpU6e2zAiGmlKKW//5VmI3bmXlsau5Jv0DIjz1sHcfORc5OF2USHRsdI8zgbq0CzRsX5fAvaM+A4+nTSH42HgPT/z+PL9+oYSn/jWRh+4aycS8ywLet3k28KzrrM/ZwNjYWDIyMro01s8++4wDBw4E3d6pnSilOHzAwrAxdegbrseTkxNwL160IRrNhcDaaDRSerY06H7tdjsfvXUhYY3WGrT336QrEhMTg9r3WFhYyIoVK7p0784opZg4caLf2e1//OMfkgF0EFNKWZVS31JK/UEp9efmV7jHJYQQYmiSAFCElVKKSy65pGUf18iRI7Farb0yG3Kq9BQnNqzD8ME/WHnqS3x5+JtooxHHlAmkZ7qxN5oYnXNxjzOBurQLjwf2nUglMmIfGAxgNnUoBD9zQSN/23aKsbkOrshL5ekn3QRajWlQBmIMMT5nA59//vlu7aM8d+5cl55Na82RA2YaG3aitcaJkyhDVKd78azKCoqW2dX4ynIqP/p7mwyinakqr6Ks5ELg5sKFzWDDqDrPrNleUlISFosl4CxvWVlZl/ZTBuO6667zmQjG4/Fw7tw50tP9zwKLAe//gDRgKbAGyARqwjoiIYQQQ5YEgCKsXnzxRY4dO9by3mAw8NWvfhWLJfjMjsHa88UeTqzfwvpzM0iylDMh7hD1X7qCxuwRaDyMm+jgpd/vorymZzMxTpwUF1qxRTcS/b274c47/RaCj7BqvveTCh7+8Qe89XISdy5N59ihwGUc2s8G1rvru7wHELqeCbQ5OC7YZyQ1/TwRERE4deC9eCZlwqZs3iLyBwtI+MNvMWxY37I0NpDKikriElslgAmiT18sFgtf+9rXAiaOCWUCmGbnzp3j008/7XD8/PnzxMTEYLUGV85CDEjZWut/A+q01n8FrgImh3lMQgghhigJAEXYuN1uTp061WHmo7i4mLVr14a8v5MlJ0mdNJnXT9/AlzPfQlvMeObOJtGYSD315Ex0cPpYAsXninvUj1M7ObAjkmEZp4mfPg1uuslvIfhmk/M1P/ivd7j8mjpuXpTBH/47Hh9JMttoPRu4p2oPdboOS0TXAueUlJQu7Xm0aztGjBQesDBm3IUyDcHU4oszxOHUTti7j3gF16XHtVka25na6lriE+Jb3nvwBF0Avr2tW7dy6tSpTtvEx8eTmZnZrfv7Y7PZ2LFjR4d/79jYWK6//vqQ9iX6nebP5kql1CQgDhgdvuEIIYQYysIaACqllimlDiqljiilHvVxXimlftN0fo9Sano4xil6x5kzZ0hMTOww82E2m9m9e3dI+9Jac+rcKaKyZ7K2ejFX/XMsjp8+TszYPNJN6SgU4y6yU10xilMlnQcHgTi1kwO7rKSknSQ2IZYGTwNu7e70mqSUJDweJ1/9TjVvbzjFls+tfGnOcPZsC7zHLUJFYPVYGTltJIWuwk4zhbaXkZHBTTfdFHT7Rt1IfbWZ2loTV+VHwsqVcOyod4lnAFGGKO8+wMmTwGxia2UD1dBhaawv02dPZ+6lc1vea3RQffpSXl7O8ePHO20zb948hg8f3q37+xMbG4vZbO4w41pTU0NaWlpI+xL9zrNKqQTgMeBd4Avgv8M7JCGEEENV2AJApZQR+D2wHJgI3KaUmtiu2XJgXNPrAeCPfTrIIaqoqIjVq1f3ajkG8AZlvrJWpqSkUFNT4zdjYnfYtZ0Fyxawe2sWsxc5iL/nahxjR5FiSsGszCQbkhk1sYbzZ4dRXV/do0ygTpwc2BXJ3Q9Oxmjx7lFrpJF6T73f+44aO4rLrvEmgskc7eIv753l/oeruO/6Yfz0XxKpr+t8yWJsbCyXLbmsZW9giaskYN3AZqtWraK+Prhi8426keMFNrJGVDPsf36J69WXMf/H/8O0aWvAa63KikKhc8bDE09w5uKZlH7jWwFnRwEK9hbQ2OCdcXRrNxZlwawCL5X1ZdiwYZ3ue6ypqeGVV17p1r0DGTduXJsspFprXnjhBWpqZDvYIPcPrXWF1nqt1nqM1joV+CTcgxJCCDE0BQwAlVIPNv3mMtRmAke01ke11g7gFeC6dm2uA17QXpuAeKWUZEroZR6Ph5KSEl577bUel0TozIgRI3wGgAaDgczMTEpLg88SGUi1vRprpJW/vR7H1bfU4tIuLMpCtIoGINoYzdiJDZw6mcDFC/K9e9W6yXWogP1bFNbSj2nUjaSb0hlvGU+0MZoaXeNdBunD+n+sx+XyZiBVCr50ey0f7iimrNTI8mmZrP3Ef8mDPdv2sHfH3pa9gWdcZwLWDWx29OjRoP6t3dqNW7s5WmAl2rmTwqo6nJEWYk6WwQsvBLzeqIxEGiK9/7bjc4lfvpSK2OC+tKz/x3pcTu+/jUM7urX/r9mwYcMoKSnxe/7cuXPY7R3LUITCVVddxeTJF7Z+nT59GovFErJ6g6LfesPHsZV9PgohhBCC4GYA04CtSqnXmpZsdj4VEbzhQOvKyMVNx7raRoTQ0aNHSUtL4+abb6axsZGjR4/2Wl8rVqzwm/r+K1/5CiNHjgxZX4eLDvO3l7axa0sES66qp1E3kmJMaUkGYlEWklLdGI2aT97c2+1MoHrjBk48sQKLq4ryZ5/AUHiMOGMcFmVhtHk0Y8xj8OCh1lPbYYau8GAhleWVbY4lpXj4xV9K+Y/fnuexB5P53r0pVJR1/LQ9e+psy7O0zxQaaDYw2EQwLlxw7CiH3zlGnPkQcWYjbquJqNOVAa9tFmeIawmu45PiqSwLfK3T6aShoYHoWG+w7sZNlOre/j/wBoD33Xef3/MlJSWkpqZ2+/6dUUqxatUqqqqqANi3bx+TJk0KmJRGDExKqVyl1I1AnFLqhlavewDJ+iOEECIsAgaAWuvH8C7BfA64BzislPqpUmpsD/v29RNP++mmYNp4Gyr1gFJqm1JqWyhnjoYSh8PBa6+9hsPhQCnFbbfdxujRo3ulL7fbTWFhITExvmdyKisrQ7YPUGvN6fLTHD84ncXL67FFekBBvDG+pY0FCwpFzkUO1n9SSXV9dbf6cq9dw4GSMYy07SUy3kbyhgNtShXEGmPJseSQakqlXte3maHrLCBauLSBD3cUE5/gYdm0TN59JYrWk7PVldXExce1uSbY2cDExMSgatC5tm6CX/2aI1vtRNdsIs5qAWXA1uCGu+4KeD1ApCGyZVZ5wpQJLFy2sGOjgwXevYVN2UGrKqqIjYttU7C+qwXgWzMYDBw9erQlCGuvsbGxV0syNDQ0sHnzZgDGjx/P1KlTe60vEXbjgauBeOCaVq/pwP3hG5YQQoihLKg9gNr7E9vZppcLSABWKqWe7EHfxcCIVu8zgfZFzIJp0zzGZ7XW+Vrr/JSUlB4Ma+g6fvw46enpLUFZfHw8Bw4caFmWGEplZWXExcVhNvvex2W321m3bl1I+nLgoLKyksKCMSxc2kCDbiDRkIhJmVraKKWwGqyMnWinvmYMp853LxGMZ9ECztSnE2cuIjbKSlze3A5tjMpImimNHEsOVoOVak81Lu0iITGhwwxga1HRmn/7RRnPrDzHH59M4L4vpXH65IXgMj4xvsM1wcwGzpo1i4ULfQRi7bi2bAS3myM1Y5idcBzr8qWoa64l4q2/wZw5Aa+HVvsAtcZoNHLs8LG2DQ4WeEtDvPhiS4mI2PhYlt+wHACP9qBQXS4A397evXv9zm5feumlvRqULViwgD179vDhhx8yevTokNcbFP2H1vod4D7gF1rrr7Z6fUdrvSHc4xNCCDE0BbMH8DtKqe3Ak8B6YLLW+pvAxcCNPeh7KzBOKZWllLIAt+LNjtbau8BdTdlAZwNVWusz7W8kQqOwsJAxY8a0ObZp0yaKior8XNF9dXV1HfpqLTk5mYqKipAEn07tJDU9jUP705i9sAEPHhKNHevlRapIxqacpPqQjTPbN3WrL/eMiymffAUXzR/FyH99BMuMeX7bWg1WxpjHMNo0GgcOJs6byOT8wKXBps60886mYqbPaeTa2Zn89fexXH/nTcTE+d8X19lsYPOMWCAN8y6m0WmjzJHI9Vm1uC5bSNRVN6HmdAxy/TEoA9GGaBx4Z5n//u7f2+6327vPWxrC42kpEdFQ19DybE6cRBuie7xkMjMzk+LijuU+7Ha7z1p9oRQTE8P9999PdnZ2r+6xFf2D1toNXB7ucQghhBDNgpkBTAZu0Fov1Vq/rrU3g4XW2oN3aUu3aK1dwIPAx8AB4DWt9X6l1DeUUt9oavYBcBQ4AvwJ+Kfu9icCmzlzZoeZjzFjxvTKPsCsrCyuuuoqv+dNJhMJCQmcP3++x305PU7s9vEkpWiSMhqxGCzYVMclhLbdBxmz60/UFSWS+cFr6I1d/wW9GzflzmRsMzKJu2hqm+WfviiliDfFk2vJJcmURGFRIXYdOAGJxQLferSSVz87zfuvWbkqP46D+zvPitk8G+jyuNrMBmqtef311wMGI3UXjeHkVY+RMaycDVd9CefY0d1KxtK8D1ApRUJSAuWlrZafNpWIwGDw/jl5EhtWbeD4keNA9wvAtzdy5Eifv9g4deoUJ0+e7PH9A4mLi2PcuHGy92/o2KCU+p1SaoFSanrzK9yDEkIIMTSZAjXQWv97J+cO9KRzrfUHeIO81seebvV3DXyrJ32I4NjtdlwuF0lJSW2Ojx49mlWrVoW8v40bN5KdnU1ny3Vvv/12v3sEu8K+dxvPfPskMyaZsWs7GcYMnz94R6zbzNiYIxTWZVNSbcexfg0RXZjdAm+mzPNnFW7n50Sr5UFfZ1ImUnQKu9/fTc53c6jx1BCpIgMGkGNznfy/pzfxp1/BnVcs5vYHqvmnRyuI6GSFpNVgxaItnHGdocpTRaYpk8jISKqqqvxmo9RaU++p53jteIaNb8CUlYVGd2svns1g8y4kV5Ccmsz5kvOkZzbtuRufC0884Z0JnDwJxudS/urfuLjsDFiAcZk92v/XbNiwYVx3Xfukw1BcXBzyAvBCAM1fSP6j1TENXBqGsQghhBjiwloIXvQfJ06c4OOPP+5wfMSIEVx55ZUh72/nzp243Z0XRzebzT2fAdy4kcoffo9jB0Yw9+TTcOwoccY4n00tsxcQG9lIjKmKvx2Pxrmwa8EfgEu7KD1rICnNTbQxukvXRkdHo1yK4a7hDDcNp5FG6jx1AWfmaqqrWHb9Cd7bUkzBXgvXzMhk24bO98g1zwY6PU4OOQ5hjjdTet5/8iQHDjSaIwURJKWeIz4xvtvF2K3KigEDHu1h+uzpjBg9om2D8blw000wPhfPgS+ofOMtEt57B/3YY3DsaI/3/4F32Wt0dDQVFRVtjhcVFYU0+6wQAFrrxT5eEvwJIYQICwkABQBnzpwhIyOjw3Gz2UxERETQhcKDobWmoqIiYPKLoqIiPvvss551tno1p0wmztTNYnrmbmK3H/RbQNw0ax6G7z7EuJx6jmdcTePUi7rcnRMnFaUm0jINWJSlS9cqpUhKSqKyopJkUzLjLeOJNcZSq2s7LUtRWV5JfGI8acPdPP36OR7+SQXfvn0Y//7tJGqqO19iaDVYiVJRjJs/jtr4Wr+ZQpv7P3LAzPCRVcQmxRJhiGiTSKcrzxltiMaJk8SURIxG/7Oc7t17mZcQiRmN26iw7j3UrT592b9/f4dEQ1/+8pfJzs4Oyf2FaKaUGqaUek4p9WHT+4lKqa+Fe1xCCCGGJgkABeAtSO0rAARYs2YNBQUFIeurtrYWi8VCRGfrFAm+Pl1nPIsWcsg9kQRLKXGpduJzZ/htq5TClj2J8ZfFU9kwnvO1XZ99dHicVJVbmbFgVLdmqi6//HLi4rwzlBZlYZR5FFlm73LLGk+Nz3p+cxfPZWLexKZngGXX1/HRzmKcLsWyaSP49L3ITvs0KAPZI7PRRu03U2ijpxGF4vABCzd+ZQIJ6QnEKd8zqcGIM8Th1E4a6ht4+U8v+53lNOZNZmpKLBgMOOIiiRk3rdt9tjd+/HgOHjyIx+N91uLiYk6dOoXJFJoAU4hWnse73735i+wh4LvhGowQQoihTQJAAcCUKVP8Ln0bPnw4p051ryyCL9HR0Tz44IMB2yUmJlJVVRVwqWhnXLPzqb38n5ky2Q3f/WciL57faftIFUnWhAbM5qk4jc4u91dd60YZFJOnZGFQXf/0Gj16dIcApLl2YJoprUPtQIAzxWcwmtrOosUlePh/fzzPz58r4ac/SOLbt6dSetb/TNuJIydY8+6alkyhhc7CNv3UeepwNZo5d9rIiaOf4cFDlLH7xdib9/FFRUehlKK2ptZnu83nqth6/a1w5524H/keUVNmdbvP9pKSkkhISODgwYMArFq1iurq7tV/FCKAZK31a4AHWpKgdf8LmxBCCNEDEgAKPB4Pubm5REf73rM2bNgwSkpKQtbf+fPn/Rbhbs1kMnHNNdf0KFW+UzvZ8oWZhDwr5rHjAy7LtBlsjJ3YwJmiZO++ty72fa5EY7VVUVlc2a3x7tu3j/fff7/DcaMyMsw0jBxLDjaDjRpPDS7twuPx8P7rHds3m7OokQ+2FzNyjJMr8zN5/fkYfD1SXGIcFWUVHfYGNs8G1uk6Th6ykTGigZIz3l8G+MqkGqwIFdGyDzB5WDLnz7aabW1VCL70bCkJ06bCTTehxowhwtDz/X+tXX311WRmZlJQUEBpaSkTJ04M6f2FaFKnlErCm/iF5rJG4R2SEEKIoUoCQEFRURF//etf/Z4fNmwY06eHLmP53r17g15SOnly4Lp4nXFqJ4VfKFJHVBNviA/Y3qIsZE1opPCgkc2rt+PA/947X7wBYDXJ8cndGm+gZa9Wg5UscxajTKNw4uRs5VlskbZOly1abZpHnqjgr387w4vPxPKVZekcP9K2fVxCHLU1tS2zrc17A8+4znDYcRi3dnOswErGyCpiE2OxKIvfvZTBUEoRa4zFoR1MuXgKtqimYLJdIfhzu/eSmp6KR3swYsRC1/ZVBjJs2DBiYmLYsWMHN954oyz/FL3lYbx1bccqpdYDLwDfDu+QhBBCDFUSAApKS0s7lH9ozWq1MnXq1Ja9Uj1VXl5OYmLHQuy+fPLJJ2zdurXbfdm1nZIzsWRP0kFl5bQoC7ZID8nD7BR+oTpNvtKe1pqzpz1YI6uJj43v1nibA8DOZh6baweOt4zHUGnAmmANqnbgxDwHb3x+ikXL6rnpkuE88/M4XC7vOaPRyLRZ03A5XS3tm2cDPXgwYKBgbwSp6aVEJUYRa4jt1vO1FqNicOEie0I2wzKGeQ+2KgTvtDsZ4XYQExeDQzuIMcT0Wt2822+/nVGjRvXKvYXQWu8AFuItB/F14CKt9Z7wjkoIIcRQJQGgoLS0tNN6fAAvv/wyhYWFIekvmAygzRITE3uUCKbOWUd5aTLjpxiDWrJoUibMykx2biPHDkbh8AQfALpxU3pGMSzTgMnQvZkkq9XK9OnTcblcAdualImL0i/ixsU3YlImajw1uHXn24pMJrjvoSreXHeK9f+wccO84ezb6Z1Vm3fpPCKsHZdYRqgIIg2R7NwcwTVfTmHy7MlEG7pW4sKXSIM3OY3D4eDP//Nn7y8YWhWCN0eYWfa121BK4VKukPQpRDgopb4FRGut92ut9wHRSql/Cve4hBBCDE0SAAoSEhIC1j5LSkoK2T7AxYsXk5qaGlTbnmYCrahzo3UUo0aYgy4fYFM2xue5cDTkUKfrgu7LvWUjddtPMWmMGSOdF3DvzLJlyzCbg1teabVamTBmAmPNYxluGo4de1C1A0eOcfHXD85y94NVfPWadH72w0S2rtvPtg3bfLZ3OGDfjgiiYvZiUAashq7X/2vPoiwYlRGj2YjZYqaspOxCIfg772TTdV+mUDf9O2hC0qcQYXK/1rqy+Y3WugK4P3zDEUIIMZRJACiYPXs2mZmZnbZJTU0NSQDodrvJyMgIWAKidb/p6end6ktrzc6tNaRn1hJl6LwUQmuRhkjGTbbjcoynUTcGd9HGjbhuvpHCjUU4t7yHceuObo0ZYO3atezZE9zqsDfffJOCggIMykCyKZkcS05QtQPBWzLixq/U8uH2Ys4Um3jo7ktZ87HvIPnA7ghGZDnYtOZjzEYzZrq//+9C/8qbcEY7GZE1ghOFJ7wnmgrBH6l1EBUThdYahepW0Xkh+gmDarV+WSllhBBvaBVCCCGCJAHgENfY2NhpAphmmZmZQS/b7My5c+d44YUXgm4fExPDFVdc0a2+XLjYtbmO2MTSLmWstCkbYyY2sHuLm6PHjvqsvdfB6tW4DZqzdXFEGc9jXP15t8YMYDAYOHv2bFBt2y+nba4dOMY8ptPaga0lD3PzP/9XwvefOMWLT1/KDx5IobK87ZeG7RusTJhSQWxSLHHGuJDtxYtVsbhwMW7CuDalLCrLK6mvqyc1PRUnTmwGW7fKagjRT3wMvKaUWqKUuhRYAXwU5jEJIYQYouQnqiGurKyMxsbAs1ypqaksWrSox/1VVFQEnQCm2dtvv825c+e63JdTOzl5xELm6AYshuB/2W5RFrJyHJwvieZscSVOHUQ9wEWLcMXYqGxMYnhsDcZLFnZ5vM2Sk5M5fz5wEXqttd9/zxhjTKe1A3259hYDD/34Oaw2N8umZfK3lVEtJSO2b4wga9wZ4lLjQroXz2b0BuaZozOZNmtay9LVirIKLpp6EQaDAad2EmOICVmfQoTBD4DPgG8C3wL+AfxLWEckhBBiyJIAcIjrSkbOV155hdpa3wW7u9JfV2cSHQ4HpaWlXe7LpV2cOh7J6Bxnl5YsmpUZs0WTllHH4X2G4EpBzJmD44XnqDFmMPLe5ag5c7s83mbJyclBzbA5nU6mTZuGxeI7uPVXO9Afg8HAXf90PT/5n3L+8Oo5fvtEAl+/cRini4xs32jlsmtsTJs7LaR78Sx49wG6tZs92/ew7tN1eDweRmePZt6SeQBoNFGG7hedFyLctNYerfUftdY3aa1v1Fo/o3WAjE1CCCFEL5EAcIiz2+1BJ2Spq6vrUUIW8AY3Y8eO7dI13U0EY9d27I0jmTTT2qWadUZlxGKwMHZCA8XH4rF7ApdYAHBcNB63KYMxC3O7PNbWkpOTue222wK2s1gsXHnllQHbta8dWKf9J4k5uP8gRw8eZfpsO+9sLmbSdDtXT0+HxkaSanYSnxhPhApdMXalFHGGOBzawZicMRTsLeD1519nz7a2eyBD2acQfU0pNU8p9Xel1CGl1FGl1DGl1NFwj0sIIcTQJAHgEJefn8/ChcEtV+xpRk6ACRMmMGbMmC5dk5KSgsPRtYLsAPWeek4dtzF+ogGj6lpWzkgVyeSZBizm6dTr+qCuKa0sp6rMyLCU7mcAbbZ27Vqqqqo6bbNz5042btwY1P1a1w5MNCRSq2t91g502B0cLjgMQEQEfOfmTbx68W08nvWvvPKdH2D64miX/y0DiTHE4MZNdEw0N919E5MvnszEqRMB7yyuWZl7VHReiH7gOeCXwHxgBpDf9KcQQgjR5yQAHOI2btxIdXV1UG1TU1OD2i/YmT//+c/U1QVfWgFgypQpXH755V3u60RxJbXVMCKj6zX5IlUkYybUsWVNPTWumqCuOXTgPBG2RiLNPU/ud/LkyYD7Hk+dOoXR2LVgzKRMDDcPZ5xlHEZl7FA7MD0zndMnT1+4YO8+xlkPMz3uIyJtZpJ3HepSf8FovaQ0ISmBiXkTW8pgyP4/MUhUaa0/1FqXaK3Lml/hHpQQQoihSQLAIW79+vVBt507dy5z53Z/b5vT6eT06dPYbMFn5ARv6YhPP/20S9dordm7s56k1HIiDV3rDyDCEEF2XCEnvoigbOf2gJk0tdYcO9JIfGJD0PUGOxPMbGtpaSkpKSndun+kIZJsczbDTcNppJF6Tz1aa5JSknA6nDTUNyWNaSrMftbuJiU+kqi8Od3qrzMWLJiV2WcRezduopUUgBcD3iql1FNKqTlKqenNr3APSgghxNDU859UxYDlcDiw2+3ExAQ3w9LQ0MD27duZP39+t/qrrKwkLi4Og6Frv3cwGAxs27aNuXPnEhkZXD0/N24OfaEZllmDVSV1eayWrbvJfOOn1Nf/jdNP/RnHo1lYZy3otL+iYx6S0uyYu1Bywp+kpKSAdRe11iQnJ3e7j+bagbHGWM64zlDhrsCmbHztu1+7MLPYVJg9afU6rBOyiMzv3v99Z5rrAVa5q3yW65AC8GIQmNX058VNfypAA5eGZzhCCCGGMgkAh7CKigri4+ODrulmNBpZvXo1c+fO7XIQB96ag6NGjerydUopkpKSKC8vDzoAdGonVeUpjLuILpWAaGb57HNMbgfp1kIKSofj2LK+8wBQu4lPvIhR40wh2SM3derUgP/G9957b4/7gQu1AxMMCZxynaK0spSyk2VMnjYZAM+4HOKyMsm0xIR8/1+zGEMM5e7yCwcOFuDZtw+VN56ICZN7pU8heptS6uGmv77f9KcGSoF1WutjQVy/DPgfwAj8r9b6Z37azQA2AbdorVf2eOBCCCEGNVkCOoQlJydz5513Bt3eYrEQGRkZ9J7B9kaMGMG1117brWsTExO7lIDGiZPy0iQmzehaBtBmatEirDUOpiQdR+tJ1M+/uNP2LlycOq5Jy/RgpOdBktls5osvvsDj8b309Ny5c2zdurXH/bQWa4wlx5JDijmFVZ+uos7p3at5+uRp3vy/N4kzxIW0v9ZsBhuapsykBwvgscdwvr2S6Ed+jNq0qdf6FaKXxTS9opteMXgTwHyolLq1swuVUkbg98ByYCJwm1Jqop92/4232LwQQggRkASAQ1h5ebnfAMOfnmQC3bVrF0VFRd26dtmyZUyc2OFnH7+cHie7N9URn1japRqALebMIfJf/5MxC2zsT72a6os6n7m0O+1sX3+O1AwnphBMrCulWLVqFeXl5T7PHzt2LOAS0e4wKiPjk8czMW0ixYeLqfHUsHvHbrInZhNl7L1afBZlwaIs3n2Ae/eB04XTZiLmeCmsXt1r/QrRm7TWP/Hx+mdgLoELwc8Ejmitj2qtHcArwHU+2n0beAMI/RcEIYQQg5IEgEPY5s2bOXLkSJeuuf766xk5cmS3+tu3bx8NDQ3dulYpxZkzZ4Ju36gbKT0bz4RJZgyqex/mtskzyLwqjR37bTR4Gjotol5SVoK9MYlhw10hWyaZnp7u95lPnz5NRkZGSPrx5ZJ5l1C+vxxrmZXjR48zKW8SFnqe3bQzMYYYHNrRkngGoxFbjRMWLerVfoXoa1rrcrz7ADszHGj9G7PipmMtlFLDgeuBp0M6QCGEEIOaBIBDWHl5OQkJCV26xmAwcP78+W71V1FR0eX+mlVWVvLhhx8G3f7kmSpcTgvZY7o/axVhiGBSPpScScHldNGg/QevpeWl1NcmkJruCskSUOg8ADxz5gzp6ekh6ceX8ePHc/PNN5MZn8m9N9xLbmxu0HtFuyvWEIsLF4zPRT/xn3DNNVhffQvmhD7zqBDhpJS6FKgI1MzHMd3u/a+BH2jtI4Vu2/4eUEptU0ptKy0tDX6gQgghBiVJAjOElZeXk5iY2KVrTp8+zZYtW7q0dxDA4/FQVVXV7QCweQ+g1jqoQOTAAScp6VVEmYJLGuOLRVnIGOnG6bRSfKSBjEm1fmvSRSVEUV8bT3pGZcgCpSlTpmC3dyzWDnDfffe11MrrDUopLBYLFouFi3Iv6rV+WmvO9qm1xpkzlsjx4zFasvukbyF6g1JqLx2DtkTgNHBXgMuLgRGt3mc2XddaPvBK09ecZOBKpZRLa/1260Za62eBZwHy8/Pbj0cIIcQQIwHgELZ48WLi4rqW2CMxMdHvvrTOKKV4+OGHMZm69yFntVoxm83U1tYGLFvh1m5KS+KZOM2CtQexmAkTRmUge0Ij508No+qiKtLxPetmjoqmrsbMsLTQzZLFxcVx/vx53G53m4LvZWVl1NTUMHr06JD11R9YlIVIQyRO7cShHSQau/bLCSH6oavbvddAmda6LohrtwLjlFJZwCngVuD2NjfTOqv570qp54H32wd/QgghRHthWQKqlEpUSv1dKXW46U+f00JKqeNKqb1KqV1KqW19Pc7BLi8vr01gEYyEhASqqqpwuztdcdRBVVVVt5eONrvmmmuCmvVyaic719cSl1jSrQygzZRS2Aw2Jk7zcPSLaBweB07t7NDOrd08+5t3SUx2YO1GyYnOvPnmmxQXF7c5tmfPni7v3Rwokg3J3n2AQJSh95LOCNEXtNYn2r1OBhn8obV2AQ/ize55AHhNa71fKfUNpdQ3enPcQgghBrdw7QF8FPiH1noc8I+m9/4s1lpP1Vrn983QRGeMRiPXXXddl7OHHjlyhJ07d/ao75ycnKDqDzpxUnhAkZxW2aMAECBSRZI+6gQfvFmFRtPg6bgPsNZdy+kTimHD3VhUaAPArKwsjh1rWy7s+PHjg272r1m0Mbrl71YlBeDF0Ka1/kBrnaO1Hqu1/q+mY09rrTskfdFa3yM1AIUQQgQjXAHgdcBfm/7+V+BLYRqH6IZJkyZ1eZ9bRUVFl/cbtrd+/XpWB1ESwOlxcrY4hrETdPdKQLQSaYhkwXInh/cPx6hNVHmqOrQpOl+E25FG6nAXESqiR/21N2bMGA4fPtzyvr6+nrNnz3Y7E2t/Z1Zmog3R2Ay2Xis6L4QQQggxlIUrABymtT4D0PRnqp92GvhEKbVdKfVAn41OdOqTTz7pchHy7iScaS/YGoSNupGycwlMmWrtcUIWszKTM8WCyeygcLeFKncVWl/IoaC1ptxZTkz0eFKjz2N++k+wcWOP+mwtKyuL6dOnt/RptVq59957sVh6tyRDOCUbk0k0yP4/IYQQQoje0GsBoFLqU6XUPh8vX4Vs/ZmntZ4OLAe+pZS6pJP+JM11H2nOyNkVs2fPZtSozoupB5KUlBRUApqSCgdgY3x2fI/6A1qWdE6bVcWmNZF48NCoG1vON+gG4lPisTUmMOzQ3zH+9L9hyZKQBYEGg4Hp06dz7tw5tNbs37+flJSUkNy7v4o1xpJkSgr3MIQQQgghBqVeCwC11pdprSf5eL0DnFNKpQM0/Vni5x6nm/4sAd4CZnbS37Na63ytdf5g/wE53IKdiWumtSYpKYno6OjAjTuRmJgY1N63XTtrGZZZS6TJ1qP+AEzKhEVZuHphFTtW1qGOHqPOcyGHQ42nhnUfreP43hqSraWYahvB4YAglqoGq7Gxkf/7v/9jxYoVbN26tdfr8QkhhBBCiMErXEtA3wXubvr73cA77RsopaKUUjHNfweuAPb12QiFX6mpqWRkZATdvq6ujj/84Q897tdsNnPVVVd12sajPezcUkts3LmQ7cezFhwjfdUPWL8zBeN//IzKA5sBb2Bb5irjRMEJyj0ZpMaUY3R5wGKBRYtC0jeAzWbj7rvvZtSoUdx6660SAAohhBBCiG4LVx3AnwGvKaW+BpwEbgZQSmUA/6u1vhIYBrzV9MOuCXhZa/1RmMYrWomJieHyyy8Pun1ZWRlJSaFZ0vfhhx8yfvx4xowZ4/O8EyfHDxkZMaahxxlAm0Vt3sPIxEqsxlIOF41k9Mdv01gfi56RT3llOQaMnCpJIOO/rsI4P9Ub/M2ZE5K+m6WmppKa6m+rrBBCCCGEEMEJywyg1rpMa71Eaz2u6c/ypuOnm4I/tNZHtdZ5Ta+LmlNgi/7hzTffpKTE58rdDkKRAKaZwWDg9OnTfs87tZOiozZGj3eHLACMnDaHmGgboyPX8I9zszDu2cf5HzxA1e511FbVYjBcjCVCM/bSEagf/jDkwZ8QQgghhBChEq4loGKAczgcBJtsJy4ujgkTJoSk32HDhnUaeDp3bKHxXCxTRlRiCtEEtzV/Huqhh7hkylE+P78AW2kt5WOTKD+2k7EOFxXrM7hi8QkiQlwDUAghhBBCiFCTAFB0S7AZOcFbyy43Nzck/aalpeF2u32f3LiR+ge/zuniGCa99RRq06aQ9GlSJiKzJ/GVny/gcO1Eal0xKGXAHhvJ6q/9M3/7NIPLzvwMy/5DIelPCCGEEEKI3iIBoOiW1NRUHA5HUG1ffPHFLpeN8CctLY2bb77Z98nVqykwxtHgNJNZVRjSTJyxhliYmM7wrGLWXfR9Iv/5BziOlLCldBRuj4kJKQVEbN4Zsv6EEEIIIYToDRIAim7Jy8tjyZIlAdtprTlx4kSPS0C0tm7dOt+zj4sWsV2PIzmyiMhaZ0gzcUYZojAajeRMP8XfivJR4yfwxdlySuxfYlna30FpzDHxIetPCCGEEEKI3iABoOgWl8vFp59+GrBdTU0NERERRESEpiQDwJkzZyguLu5w3DN7FgcyL2f4sDIsD/8gpMlYrMqKQvGl262s/yyOhgYHp4rOsL3yeq5J+wClFMbzlSHrTwghhBBCiN4gAaDoFqPRyNatW2loaOi0XUNDA1lZWSHte/jw4Zw6darDcdeWDdj3O8mJOIL50cdg48aQ9WlURiINkcy+Ip7kVDsfv2Ule8HDRJocTIovQJvMmGbPC1l/QgghhBBC9AYJAEW3KKVISkri/PnznbYbNmwYN954Y0j7zszM9DkD6Niwlmr7KMYlnMJcWRvSPYAACYYE3AYXD/9E8+Izabz9+WSu/5oTfdedqO8+hHnm3JD2J4QQQgghRKhJACi6LTU1NWAtwB07dnDy5MmQ9puZmck999zT4fjpCePZVTKMMdEnMWlDSPcAAkQaIkHDFdfVUXbKzdv/Z+PaK09jv/4q4sZNw6iMIe1PCCGEEEKIUJMAUHTbFVdcQV5eXqdt9u7di9PpDGm/BoOBkydPdph9PBJto9KTQ/Z1k+Ef/wh5QfYIFeEN8o58wTcTf868+A2k/+77uI8eJtEYmkL3QgghhBBC9CYJAEW3GY1GTpw40WmbkpISUlNTQ973sWPH2L17d5tje/cX49YWRnzt+pAHf+Bd9hpviMdx+Au+nPEGT0/7Nm7twVhwiEgVGfL+hBBCCCGa2bWdD2s/ZHfjblzaFe7hiAFMAkDRbU6nk5UrV6K19nm+rq4Oj8cT0hIQzXJycjh8+HCbY9V1qYwca8dmsIa8v2axxlhcuTlgNmE0gj0llsSsqRiUfCoJIYQQovdsbdjKIechVjes5i9Vf+GkM7RbbMTQIT+1im6LiopCKUVtba3f89/97ndRSoW878zMTGpra1sKzHs8HmISpzN6nAuLwRLy/prZlA3D2LHoJ/4T7rwT9/ceIi5vfq/1J4QQQghR6a5kp30nEywTuDH6RqzKytu1b7OlYYvfX8QL4Y8EgKLblFIMGzaMc+fO+Tx/6tQpKioqeqVvg8HA1772NRITvXvvXlzxInu3NTIy24EZc6/0CWBSJhIMCTSMG4XzxuuwZV+ETdl6rT8hhBBCiM8bPseIkXm2eWSaM7kl9hbGmcexsXEj79a9S6OnMdxDFAOIBICiRy699FK/e/y2bt3qs15fqCQkJLB7927eeecdzpefp7IsmZHZdsyq9wJAgCRjEm7c2LWdFENKr8xwCiGEEEIAnHSe5KjzKDOsM4gyRAFgURaWRS1jkW0RJ50nWVGzgnMu37+QF6I9CQBFj2RmZvpdelBcXExmZmav9p+amorNZuPG226kqDCCrLHuXi/HYDPYiDHEoNHEGGN6tS8hhBBCDF0e7WFtw1piDbFMs05rc04pRZ41j5tjbsajPbxe8zp77XtlSagISAJA0SO1tbU888wzHb7YNDQ0UF1dTUpKSq/2n5GRwRVXXIEt3sbJoxHkjOub2bhhpmGkmdIwKVOf9CeEEEKIoWefYx9l7jLm2+b7/ZkjzZTG7bG3M9w0nM/qP+Pv9X/HqUNbgksMLhIAih6JiYnBZDJ12OtnNpu56667MBj65kPsXLkdl0OROaz3EsC0FmWIYphpWJ/0JYQQQoihp9HTyMaGjWSaMsk2Z3fa1mawcV30dcyyzuKA4wCv1rxKhbt38jCIgU8CQNFjo0eP5ujRo22OlZeX9/rsX2sHD2sye7kEhBBCCCFEX9nUuAm7trMwcmFQ+QYMysBs22y+FP0l6jx1vFL9CkccR/pgpGKgkQBQ9Fh+fn5LNs5mb731FmfPnu2T/rXWHDkMo8Y6MBt6NwGMEEIIIURvO+8+zx77HiZHTCbZmNyla0eZR3Fb7G0kGBP4W93f+Lz+c9za3UsjFQORbGASPTZy5EjcbjcejweDwUBNTQ0VFRW9ngCmmRs3JwstjMq2Y5aSDEIIIYQYwLTWrKlfQ4SKYI51TrfuEWuI5aaYm/i84XN22Hdw1n2W5VHLiTZEh3i0YiCSGUAREq+//jp79+4FYOfOnVx00UUYjb2bjbOZUzs5cSSCkWN7twagEEIIIURvO+I8QrGrmDm2OVh7sLXFpEwsjlzM0qillLhKeLn6ZYqdxSEcqRioJAAUIXHxxRezbt06XC4XOTk5zJs3r8/6dmonJwstZGW7MSj5kBZCCCHEwOTUTtbWryXZmMwky6SQ3DPXksutsbdiVVberH2TrY1bpVTEECc/LYuQyM7OJi0tjZdeeonU1NQOewJ7k0M7KCrsuxIQQgghhBC9YXPDZmp1LYsiF4X0l9pJxiRujb2VceZxbGjYwLt171LvqQ/Z/cXAInsARUgopbjhhhuor6/vs9IPzc6U2XE5FZnDIvq0XyGEEEKIUCl1lbLDvoNJlkkMNw0P+f0tysKyqGVk2DP4vOFzXqx+kcsiL2OMZUzI+xL9m8wAipBRShEVFdXn/R464mFEtpSAEEIIIcTA5NEe/lH/D6zKyjxb722jUUqRZ83jttjbiDJE8V7de3xW95kUjh9iwhIAKqVuVkrtV0p5lFL5nbRbppQ6qJQ6opR6tC/HKAaOw4dg1Fg7ZiUJYIQQQggx8Oy17+Wc+xyXRF7So8QvwUoyJnFLzC1Mj5jOXsdeVlSv4JzrXK/3K/qHcM0A7gNuANb6a6CUMgK/B5YDE4HblFIT+2Z4YqBwaRfHC83eDKASAAohhBBigKn11LKhYQMjTSMZbx7fZ/2alIkFkQu4IfoGnNrJazWvsaVhCx7t6bMxiPAISwCotT6gtT4YoNlM4IjW+qjW2gG8AlzX+6MTA4lLuygqjGBktpSAEEIIIcTAorVmVf0q3LhZHLkYpfo+od0I8wjuiL2DseaxbGzcyMqalVS4K/p8HKLv9Oc9gMOBolbvi5uOCdHCiZMTRyyMHecJyxdNIYQQQojuOug8yFHnUeba5hJvjA/bOKwGK8ujlrM0cinlnnJeqn6J7Y3bZTZwkOq1LKBKqU+BNB+n/lVr/U4wt/BxzG/REqXUA8ADACNHjgxqjGLgc3gcFBXGMX5s3xSdF0IIIYQIhTpPHWvq15BuTGdqxNRwDwelFLkRuYwwj+Cz+s9Y17COI44jXB51OYnGvivvJXpfrwWAWuvLeniLYmBEq/eZwOlO+nsWeBYgPz9fqlsOEWfK7LjdMHyYJdxDEUIIIYQIitaaz+q92Tcvj7o8pDX/eirKEMXVUVdzyHmI1fWrebn6ZWbbZjM9Ynq/Gqfovv78v7gVGKeUylJKWYBbgXfDPCbRzxw87GFkth2rQWoACiGEEGJgaF76Occ2hwRjQriH04FSivGW8dwZeyejzaNZ37Ce12pe47z7fLiHJkIgXGUgrldKFQNzgL8ppT5uOp6hlPoAQGvtAh4EPgYOAK9prfeHY7yi/zp8GEaMkQygQgghhBgYGjwNrKlfQ5oxjWkR08I9nE5FGaK4Kuoqlkctp9pTzYrqFaxvWC91Awe4XlsC2hmt9VvAWz6OnwaubPX+A+CDPhyaGEDc2s2JQjOjsh2YVXS4hyOEEEIIEdCWxi3YtZ0lUUsGxJJKpRQ5lhxGmEbwecPnbGvcxiHHIRZHLma0eXS4hye6of9/1Anhh0u7OHnEwqhsB6bw/C5DCCGEECJoFe4K9tj3cJHlIpKNyeEeTpfYDDauiLqCG6JvwICBd2rf4cPaD6nz1IV7aKKLJAAUA1ZLCYhsLSUghBBCCNHvbWjYgBEjs22zwz2UbmuuGzjbOptCZyEvVL/AHvsetJYcjAOFBIBiwHJ4HBQdjSB3nJSAEEIIIUT/Vumu5IjzCFOtU4kyRIV7OD1iUiZm2WZxR+wdpBpTWVW/ildrXuWs62y4hyaCIAGgGLBOn7fj8cDwFMkAKoQQQoj+bZd9F0aM5EXkhXsoIZNgTOCG6BtYGrmUWk8tr9a8yid1n8iy0H5ONk6JAevgYQ8jxtiJMEgNQCGEEEL0X42eRvbb95NjyRnws3/tNReQH2MZw5aGLey076TQUcgs2yzyIvIwKlmp1d/IDKAYsI4cgZHZUgJCCDE4KaWWKaUOKqWOKKUe9XH+DqXUnqbXBqXU4JlWEGKQ+cLxBS5c/b7sQ09YlIX5kfO5M/ZOMkwZfN7wOS9Vv8Rx5/FwD020IwGgGJA82sOxI6amEhASAAohBhellBH4PbAcmAjcppSa2K7ZMWCh1noK8J/As307SiFEsE44T5BkSCLFlBLuofS6BGMC18Vcx7XR1+LBwzu17/BOzTuUucvCPTTRRAJAMSA5cXKy0MKosU5MSlYyCyEGnZnAEa31Ua21A3gFuK51A631Bq11RdPbTUBmH49RCBEEt3Zz2nWaEeYR4R5Kn8oyZ3Fn7J3Mt83ntPs0L1W/xKd1n8r+wH5AAkAxIDm1twTEuHHhHokQQvSK4UBRq/fFTcf8+Rrwoa8TSqkHlFLblFLbSktLQzhEIUQwzrrO4sJFpmno/Y7GpExcbL2Ye2LvIS8ijwOOAzxf9TwbGzbi0I5wD2/IkqkTMSA53E6KCmMYP05+hyGEGJR8FTf1WWRLKbUYbwA439d5rfWzNC0Pzc/Pl0JdQvSxIpf3dznDTZ39DmdwsxlsLIxcSF5EHhsaNrClcQv77PuYZZvFJMskDEp+nutLEgCKAelsuQOtISNZSkAIIQalYqD1erFM4HT7RkqpKcD/Asu11rLBRoh+qNhVTKoxFavBGu6hhF28MZ4ro6/krOssnzd8zqr6Vexs3Mks2yxyzDkSCPYR+VcWA1LBITcjxtqJMEoJCCHEoLQVGKeUylJKWYBbgXdbN1BKjQTeBL6itT4UhjEKIQJwaRdnXWeH5PLPzqSZ0rgp+iauiboGkzLxcd3HvFz9MkccR9BaFir0NpkBFAPS4cOaUdl2zESGeyhCCBFyWmuXUupB4GPACPxZa71fKfWNpvNPA/8OJAF/UEoBuLTW+eEasxCio7Ous7hxk2mWALA9pRRjLGPIMmdx2HmYTQ2b+Fvd30gxpjDHNofRptE0fW0TISYBoBhwPNrDsUITI8c6pQSEEGLQ0lp/AHzQ7tjTrf5+H3BfX49LCBG88+7zAKQaU8M8kv5LKUWOJYdsczYHHQfZ1LiJd2vfJc2YxmzbbEaaRkogGGISAIoBx4WLE0csXLK0DqMyhns4QgghhBA+lbnLsCorkUpWLAViUAYmREwgx5LDF44v2NKwhbdr3ybVmMpM60zGmMdIIBgiEgCKAaelBMSDUkdGCCGEEP1XmbuMJGOSBC5dYFRGJkdMZoJlAgWOArY1buP9uvdJMiYx0zqTbHO2JIvpIQkAxYDj8DgpKowmN1s+fIUQQgjRP2mtKXOXkRuRG+6hDEgmZWJSxCQmWiZyyHGIrY1b+bDuQ+IN8cywzmC8ZbysBOsm+QlaDDinz9tRKpr0ZMkAKoQQQoj+qVbX4sBBkjEp3EMZ0AzKQG5ELuMt4zniPMLWxq38vf7vbGzYyFTrVCZFTCJCSVmwrpAAUAw4Bw95GDG2UUpACCGEEKLfKnN7S3MmGSQADAWlFOMs48g2Z3PCdYLtjdtZ17COLQ1buCjiIqZapxJriA33MAcECQDFgHO4UDNyrAMzUeEeihBCCCGETy0BoMwAhpRSitHm0Yw2j6bEVcIO+w522Xexy76LceZxTLdOZ5hpWLiH2a9JACgGFK01Rw8bGZntwKTiwj0cIYQQQgifytxlRKkorAZruIcyaKWaUllmWsZc21x2N+5mn30fh5yHyDBlkBeRx1jzWNkn6IMEgGJAceLNALp4eb18QgshhBCi32rOACp6X6whlgWRC5hpm8l++35223fzYd2HRKkoJkdMZlLEJKIMsnKsmQSAYkBxaicnCy2My24I91CEEEIIIXzyaA/l7nImR0wO91CGlAgVwXTrdKZGTOWE6wS7G3ezqXETWxq3MM4yjryIPNKMaUO+LIcEgGJAcXpcFBVGMX6c1H8RQgghRP9U4anAhYtUY2q4hzIkGZSBLHMWWeYsKtwV7LHv4Qv7Fxx0HCTZmMxFlovIteQO2eW5EgCKAeV0qQNliCIjWdL9CiGEEKJ/Ouc6B3j3qInwSjAmsDByIXNsczjoOMg++z7WNKxhXcM6si3ZTLJMYrhp+JCaFQxLAKiUuhl4HJgAzNRab/PT7jhQA7gBl9Y6v6/GKPqngsMuRoxpxGKQEhBCCCGE6J9K3CWYMZNgSAj3UEQTi7IwOWIykyMmU+IqYb9jPwWOAg46DhJviOeiiIuYYJkwJPYKhmsGcB9wA/BMEG0Xa63P9/J4xABx5AhNGUAH/yenEEIIIQamc65zpJpSh9Ss0kCSakol1ZTKfNt8jjiOsN+xn/UN69nYsJEscxa5llxGm0djUoNzsWRYnkprfQCQTwrRJVprCg8bGZ3txIw53MMRQgghhOjArd2UukuZEjEl3EMRAZiVmQkRE5gQMYEKdwX77PsocBRQ6CwkQkUwzjyOXEsuGaaMQRW39PewVgOfKKU08IzW+tlwD0iEjwsXJwrNLF5ej0FJEhghhBBC9D/l7nLcuKUY+QCTYExgQeQC5tnmUeQqalkeus+xjxhDDOMt48m15A6K0h69FgAqpT4F0nyc+let9TtB3mae1vq0UioV+LtSqkBrvdZPfw8ADwCMHDmyW2MW/ZtTOzlRaCFnnJSAEEIIIUT/dM7dlABGMoAOSAZlYJR5FKPMo3BGOil0FlJgL2B743a2NW4jxZjCeMt4ss3ZxBnjwj3cbum1AFBrfVkI7nG66c8SpdRbwEzAZwDYNDv4LEB+fr7uad+i/3F6XBQdiSQ3RwrACyGEEKJ/KnGVYFEW4g3x4R6K6CGzMpNrySXXkkudp47DjsMUOApY17COdQ3rSDGmkG3OJtuSTaIxMdzDDVq/XQKqlIoCDFrrmqa/X8H/b+/uYtu6zzuOfx8evkiyY9mWZVu241cpdmancYzMSTo0KNZmbY2uaYEN6FWybkAaYLlvigC7KAZs3a66LdtQFAVaYF13ldXYkrXphiFAFw9OAr8uiUX5RXak2JJjO3YskYfkswvSimxREm2JOoc8v09A8PDwmHoe/2U+echz/n/4XsRhSYQ+GCuQCrro69ESECIiIhJPo+VR1gXr2uqaMYFlqWXs7djL3o69fFz+mHyYJ1/M8+bkm7w5+SarUqvoz/bTn+mnN+iN9fhHtQzEN4C/BXqBfzezI+7+JTPbAPzI3Q8A64BXan95aeBn7v4fUcQr8fDeYJnNOybJmCaAERERkfiZrEwyXh7n8Y7How5FmmhFsIJ9wT72dezjRuUGQ8Uh8mGetybf4vDkYbpT3VML0W9MbySweJ29FtUsoK8Ar9TZPwIcqG2fBh5e4tAkxgYHq0tAZGx51KGIiIiIzDBSGgFgU3pTxJHIUlmeWs7DHQ/zcMfDTFQmGAqHGCoOcbxwnCOFI2TJsjmzmW2ZbWzNbKUr1RV1yPE9BVRkOnfndD7Flh1aAkJERETi6ULpAgGBZgBNqM5UJ3tye9iT20PoIefD85wJz3AmPEM+zAPQF/SxNbOVbZltrAnWRHKqqBpAaQllypzNZ3jqqxOxPqdaREREkuuD0gf0pfvadgFxaVzGMmzPbmd7djvuzlh5bKoZvHXdYJd1sSWzhc3pzWzObF6ybwf12yktIfSQ86ezDPRPRh2KiIiIyAwFLzBWHmN/x/6oQ5GYMTPWpteyNr2Wxzof45PKJ5wNzzIcDnMmPMO7xXcB6A16pxrCDekNTbt2UA2gtIRiJWQ438WuAf3KioiISPyMlEZwnI3pjVGHIjG3LLWM3bnd7M7txt25VL7EufAcw6Vh3pl8h7d5m293f1sNoCTbyKWQIO2s78lGHYqIiIjIDMPhMAEBfem+qEORFmJmrEuvY116HfvZT9GLjJXGyKWat+xZqmmvLLKI3suX2LyjoCUgREREJHbcnaFwiC2ZLbr+TxYka1k2Zpr7LbIaQGkJg4Nw/46iGkARERGJnbHyGNcr19me2R51KCLzUgMoLSE/aGztL5LWWcsiIiISM0PhEIapAZSWoAZQYq/kJc4NZdgx4FoCQkRERGJnqDjEhvQGOlOdUYciMi99nSKxF3rI8FCWgf5C1KGIiIjIInB3rlWucdNvkiFD1rJTt2bNfNgsl8uXuVy5zJO5J6MORaQhagAl9ooeMpxfxoMDE1GHIiIiIvfI3TkdnuZU8RTnSucoeP0PdgMCspYlY9MaQz5tEG/bf+e+O45biglZDk0cIkOGndmdTf9ZIotBDaDE3ujFEplshXWrtQSEiIhIKxopjfDGzTe4WL5Ip3WyPbOdvnQfK1IrKHqRohcJPZzaLnL7vpt+k6uVq1P7QsKGfm5AcFvDeOe3jXWbyGmN5PR9AcGMS1FGS6PkwzyPdTxGV6qrGX91IotODaDE3nuDZe7friUgREREWk2hUuA3k7/heOE4y205T3U9xa7sLlK2sGkoKl4hZFrDWK+JnNZMTt8/4RNcq1yb2tdoM5kidXuzSJbrlet0Wif7OvYtKB+RpaQGUGLv/cEKm/uLZGxF1KGIiIgkwnh5nJOFk3xU/ohJn2RFagVrgjX0BD2sCdbQneqec2K265XrHJk8wonCCYoU2ZvbyxOdT5C1xTmbJ2UpcuTI2cIXy57eTNZrIEMPKXhhRsMZesh9qft4pOORRctLZCmoAZTYG8obW/tDAlrronAREZFWUvIS+WKeY4VjjJZHCQhYE6yhwzoYK4+RD/NTx6ZJ0xP0sDpYPXV6ZGABJS/xceVjzoRncJyBzACPdjxKb7o3wszmtpjNpEgrUAMosVbyEufyGb70tYKWgBAREVlkZS8zXBrmVPEUQ8UhQkK6U918rvNzPJh98LZlDUIPqzNeli8zXh7ncvky58PzlChR8hJlygQEdKW6+EzuMzySe4QVgc7eEYkbNYASa9U1AHM8MFCMOhQREZG2MVGZ4HjhOEcLR7npN8lZjgeyD7Azu5NN6U11P3TNWIb16fWsT6+PIGIRWSxqACXWih5yfqiLXf1aAkJERGShxsvjHCsc493Cu5QosSW9hYdyD7Els2VJlkwQkejpX7rE2siH1SUg1vZoBlAREZF7UfACg8VBThROcLF8kYCAndmd7OvYR0/QE3V4IrLE1ABKrL03WGbzjgIZ1ACKiIg0KvSQM+EZThVPcTY8S5kyPakenux8kl3ZXbdd2yciyaIGUGLtVF5LQIiIiDTiWvkaZ8OznCudm5qcpcu62JPbw87sTtYH6zWhmoioAZR4yw/Clh2hrksQERG5w0RlgtHSKOdL5zkXnuNK5QoA3aludud205/pZ0N6w4IXXReR9qL/q5bYKnuZs/kMX/l6IepQREREIlXxClcrV/mw9CEjpRFGS6N8VPkIgICATelNPJR7iK2ZraxMrdQ3fSIyKzWAEluhhwyfzrFzIIw6FBERkSUzWZnkSuUK4+VxxkpjjJXHGC+PU6IEQM5y9AV97MruYkN6A+vS63SmjIg0TO8WEluhlzif72RX/2TUoYiIiCwad2fSJ7lRucHVylWulK9wtXKVq+WrXKlcYdI/rXtZy9Ib9LInt4feoJe16bX0pHr0DZ+I3LNIGkAz+2vg94EiMAR8y92v1jnuy8APgAD4kbv/5VLGKdG6MBqS7cjRu1ozgIpI8sxXA63aAfwAOADcBP7I3d9Z8kBlyq3GbsInmKhMcNNvMuETfFL5hOuV69yo3Ji6v/Vt3i3LbBmrglX0Z/pZFaxiZWolPUEPK1Ir1OyJyKKK6hvA14HvunvJzL4PfBf4zvQDzCwAXgaeAi4Ah83soLv/35JHK5F4P68lIEQkmRqsgV8BBmq3x4B/qN3LPXB3ypQpeYkSJYpepOhFCl647f7O7UmfZKIyUW36fALHZ7y2YSyzZSxPLac36GVbZhvLU8u5L3Uf3aluVgYryVo2gqxFJIkiaQDd/VfTHh4C/qDOYfuBvLufBjCznwNPA2oAE+LUYIX7dxTJmNYqEpHEaaQGPg381N0dOGRmK82sz91HmxVUxSuUKOHuzPnftOeBWZ+b68/d+rMVKlS8QoUKZcqfbnu5+twd2xWvHVfbLlGqNnW1xu62+zv2NSpDhpzlyFqWnOXoDrpZb+vpSnXRaZ3VW6qTLuuiM1V9HFjQlDEREblbcbgG8I+Bf6mzfyNwftrjC+iTzUTJ52Frf6iiKSJJ1EgNrHfMRqBpDWA+zPPaJ6816+UXzDBSpAgISFmKFCnSliZNunpvabKWpcu6bttXbztr2anbVLNHjoxltKyCiLS0pjWAZvZrYH2dp15y91/UjnkJKAH/VO8l6uybeV7Fpz/vOeC52sMbZvb+3UU8wxpgfIGv0Qpin+fL31vwS8Q+x0WShDyTkCMoz7uxZTECiaFGamBDdVL18Z4pz/aRhBxBebaTxcqxbo1sWgPo7l+c63kzexb4KvCF2ukrd7oA3D/t8SZgZI6f90Pgh/cQ6mzxveXujy7W68VVEvJMQo6QjDyTkCMoTwEaq4EN1UnVx3ujPNtHEnIE5dlOmp1jJOcw1GY2+w7wNXe/Octhh4EBM9tmZlngm8DBpYpRREQkQo3UwIPAM1b1OHCtmdf/iYhIe4jqGsC/A3LA67WpjQ+5+/NmtoHqVNcHajOEvgD8kuoU2D9295MRxSsiIrJkZquBZvZ87fl/BF6lugREnuoyEN+KKl4REWkdUc0C2j/L/hGqxezW41epFrgoLNrpMjGXhDyTkCMkI88k5AjKU6hfA2uN361tB/50qeMiOeOmPNtHEnIE5dlOmpqj1b/8TkRERERERNqN5jEWERERERFJCDWANWb2h2Z20swqZjbrrDtmdtbMjpvZETN7ayljXKi7yPHLZva+meXN7MWljHExmNlqM3vdzAZr96tmOa7lxnK+salNBvE3teePmdm+KOJcqAby/LyZXauN3REz+7Mo4lwIM/uxmV0ysxOzPN8uYzlfni0/lu0uCfURVCPrHNdy46kaOfV8y7+vJqFGRlof3V236mmwDwI7gf8GHp3juLPAmqjjbVaOVCcbGAK2A1ngKPBbUcd+l3n+FfBibftF4PvtMJaNjA3Va2hfo7o+2OPA/0Ydd5Py/Dzwb1HHusA8nwT2ASdmeb7lx7LBPFt+LNv9loT62GieqpHxvalG3nZMy7+vJqFGRlkf9Q1gjbu/6+4LXRw31hrMcT+Qd/fT7l4Efg483fzoFtXTwE9q2z8Bvh5dKIuqkbF5GvipVx0CVppZ31IHukDt8Ds4L3d/A/hojkPaYSwbyVNiLgn1EVQj24BqZBtJQo2Msj6qAbx7DvzKzN42s+eiDqYJNgLnpz2+UNvXStZ5bS2s2v3aWY5rtbFsZGzaYfwazeEJMztqZq+Z2e6lCW1JtcNYNqrdxzIpWu099V60w79L1ci5j4k71ciqdhjLRjRlHKNaBzASZvZrYH2dp15y9180+DK/4+4jZraW6jqG79U6+FhYhBytzr7YTRU7V5538TKxHss6Ghmblhi/eTSSwzvAFne/YWYHgH8FBpod2BJrh7FsRBLGMvaSUB9BNRLVyJYYv3moRla1w1jOp2njmKgG0N2/uAivMVK7v2Rmr1D9Kj42b4iLkOMF4P5pjzcBIwt8zUU3V55mdtHM+tx9tHY6wKVZXiPWY1lHI2PTEuM3j3lzcPePp22/amZ/b2Zr3H18iWJcCu0wlvNKyFjGXhLqI6hGgmpkA8fEnWpkVTuM5ZyaOY46BfQumNkyM7vv1jbwe0DdmXta2GFgwMy2mVkW+CZwMOKY7tZB4Nna9rPAjE91W3QsGxmbg8AztdmxHgeu3TrVp4XMm6eZrTczq23vp/pednnJI22udhjLeSVkLNtei76n3gvVyPhSjaxJyPtqO4zlnJo6js2YWaYVb8A3qH6aUAAuAr+s7d8AvFrb3k51tqWjwEmqp4xEHvti5lh7fAA4RXWWqZbKsRZ/D/CfwGDtfnW7jGW9sQGeB56vbRvwcu3548wxY1+cbw3k+UJt3I4Ch4DPRh3zPeT4z8AoENb+Xf5Jm47lfHm2/Fi2+y0J9bHRPGuPVSNjelONbJ/31STUyCjro9V+gIiIiIiIiLQ5nQIqIiIiIiKSEGoARUREREREEkINoIiIiIiISEKoARQREREREUkINYAiIiIiIiIJoQZQREREREQkIdQAioiIiIiIJIQaQJEWZma/bWbHzKzDzJaZ2Ukz2xN1XCIiIlFTjRSpTwvBi7Q4M/tzoAPoBC64+19EHJKIiEgsqEaKzKQGUKTFmVkWOAxMAp9193LEIYmIiMSCaqTITDoFVKT1rQaWA/dR/ZRTREREqlQjRe6gbwBFWpyZHQR+DmwD+tz9hYhDEhERiQXVSJGZ0lEHICL3zsyeAUru/jMzC4D/MbPfdff/ijo2ERGRKKlGitSnbwBFREREREQSQtcAioiIiIiIJIQaQBERERERkYRQAygiIiIiIpIQagBFREREREQSQg2giIiIiIhIQqgBFBERERERSQg1gCIiIiIiIgmhBlBERERERCQh/h8YuO4/RUSr5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plot_data(x_train, y_train, x, f(x))\n",
    "plot_prediction(x_test, \n",
    "                expected_output, \n",
    "                aleatoric_uncertainty=aleatoric_uncertainty)\n",
    "plt.ylim(-2, 2)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plot_uncertainty(x_test, \n",
    "                 aleatoric_uncertainty=aleatoric_uncertainty)\n",
    "plt.ylim(0, 1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian neural network without NCPs\n",
    "\n",
    "In a Bayesian neural network, we infer a posterior distribution $p(\\mathbf{w} \\mid \\mathbf{x}, \\mathbf{y})$ over weights $\\mathbf{w}$ given training data $\\mathbf{x}$, $\\mathbf{y}$ instead of making point estimates with ML or MAP. In general, the true posterior $p(\\mathbf{w} \\mid \\mathbf{x}, \\mathbf{y})$ is untractable for a neural network and is often approximated with a variational distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta}, \\mathbf{x}, \\mathbf{y})$ or $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ for short. You can find an introduction to Bayesian neural networks and variational inference in [this article](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks.ipynb).\n",
    "\n",
    "Following the conventions in the linked article, I'm using the variable $\\mathbf{w}$ for neural network weights that are random variables and $\\boldsymbol{\\theta}$ for the parameters of the variational distribution and for neural network weights that are deterministic variables. This distinction is useful for models that use both, variational and deterministic layers. \n",
    "\n",
    "Here, we will implement a variational approximation only for the `mu` layer i.e. for the layer that produces the expected output $\\mu(x, \\mathbf{w}, \\boldsymbol{\\theta})$. This time it additionally depends on weights $\\mathbf{w}$ sampled from the variational distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$. The variational distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ therefore induces a distribution over the expected output $q(\\mu \\mid x, \\boldsymbol{\\theta}) = \\int \\mu(x, \\mathbf{w}, \\boldsymbol{\\theta}) q(\\mathbf{w} \\mid \\boldsymbol{\\theta}) d\\mathbf{w}$. \n",
    "\n",
    "To generate an output at input $x$ we first sample from the variational distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ and then use that sample as input for $p(y \\mid x, \\mathbf{w}, \\boldsymbol{\\theta}) = \\mathcal{N}(y \\mid \\mu(x, \\mathbf{w}, \\boldsymbol{\\theta}), \\sigma^2(x, \\boldsymbol{\\theta}))$ from which we finally sample an output value $y$. The variance of output values covers both epistemic and aleatoric uncertainty where aleatoric uncertainty is contributed by $\\sigma^2(x, \\boldsymbol{\\theta})$. The mean of $\\mu$ is the expected value of output $y$ and the variance of $\\mu$ represents epistemic uncertainty i.e. model uncertainty.\n",
    "\n",
    "Since the true posterior $p(\\mathbf{w} \\mid \\mathbf{x}, \\mathbf{y})$ is untractable in the general case the predictive distribution $p(y \\mid x, \\boldsymbol{\\theta}) = \\int p(y \\mid x, \\mathbf{w}, \\boldsymbol{\\theta}) q(\\mathbf{w} \\mid \\boldsymbol{\\theta}) d\\mathbf{w}$ is untractable too and cannot be used directly for optimizing $\\boldsymbol{\\theta}$. In the special case of Bayesian inference for layer `mu` only, there should be a tractable solution (I think) but we will assume the general case here and use variational inference. The loss function is therefore the negative variational lower bound.\n",
    "\n",
    "$$\n",
    "L(\\boldsymbol{\\theta}) = - \\mathbb{E}_{q(\\mathbf{w} \\mid \\boldsymbol{\\theta})} \\log p(\\mathbf{y} \\mid \\mathbf{x}, \\mathbf{w}, \\boldsymbol{\\theta}) + \\mathrm{KL}(q(\\mathbf{w} \\mid \\boldsymbol{\\theta}) \\mid\\mid p(\\mathbf{w}))\n",
    "\\tag{5}\n",
    "$$\n",
    "\n",
    "The expectation w.r.t. $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ is approximated via sampling in a forward pass. In a [previous article](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks.ipynb) I implemented that with a custom `DenseVariational` layer, here I'm using `DenseReparameterization` from Tensorflow Probability. Both model the variational distribution over weights as factorized normal distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ and produce a stochastic weight output by sampling from that distribution. They only differ in some implementation details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_model(n_hidden=200):\n",
    "    leaky_relu = LeakyReLU(alpha=0.2)\n",
    "    \n",
    "    x_in = Input(shape=(1,))\n",
    "    x = Dense(n_hidden, activation=leaky_relu)(x_in)\n",
    "    x = Dense(n_hidden, activation=leaky_relu)(x)\n",
    "    m = tfpl.DenseReparameterization(1, name='mu')(x)\n",
    "    s = Dense(1, activation='softplus', name='sigma')(x)\n",
    "    d = Lambda(lambda p: tfd.Normal(loc=p[0], scale=p[1] + 1e-5))((m, s))\n",
    "\n",
    "    return Model(x_in, d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = create_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implementation of the loss function follows directly from Equation $(5)$. The KL divergence is added by the variational layer to the `model` object and can be obtained via `model.losses`. When using mini-batches the KL divergence must be divided by the number of batches per epoch. Because of the small training dataset, the KL divergence is further multiplied by `0.1` to lessen the influence of the prior. The likelihood term of the loss function i.e. the first term in Equation $(5)$ is computed via the distribution returned by the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_size = x_train.shape[0]\n",
    "batch_size = 10\n",
    "batches_per_epoch = train_size / batch_size\n",
    "\n",
    "kl_weight = 1.0 / batches_per_epoch\n",
    "\n",
    "# Further reduce regularization effect of KL term\n",
    "# in variational lower bound since we only have a \n",
    "# small training set (to prevent that posterior\n",
    "# over weights collapses to prior).\n",
    "kl_weight = kl_weight * 0.1\n",
    "\n",
    "@tf.function\n",
    "def train_step(model, optimizer, x, y, kl_weight=kl_weight):\n",
    "    with tf.GradientTape() as tape:\n",
    "        out_dist = model(x, training=True)\n",
    "        nll = -out_dist.log_prob(y)\n",
    "        kl_div = model.losses[0]\n",
    "        loss = tf.reduce_sum(nll) + kl_weight * kl_div\n",
    "        \n",
    "    optimizer.apply_gradients(backprop(model, loss, tape))\n",
    "    return loss, out_dist.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After training, we run the test input `x_test` several times through the network to obtain samples of the stochastic output of layer `mu`. From these samples we compute the mean and variance of $\\mu$ i.e. we numerically approximate $q(\\mu \\mid x, \\boldsymbol{\\theta})$. The variance of $\\mu$ is a measure of epistemic uncertainty. In the next section we'll use an analytical expression for $q(\\mu \\mid x, \\boldsymbol{\\theta})$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1000: loss = 10.245, mse = 0.131\n",
      "epoch 2000: loss = 3.361, mse = 0.094\n",
      "epoch 3000: loss = 1.265, mse = 0.086\n",
      "epoch 4000: loss = 0.040, mse = 0.079\n",
      "epoch 5000: loss = -0.773, mse = 0.069\n",
      "epoch 6000: loss = -1.527, mse = 0.060\n",
      "epoch 7000: loss = -2.112, mse = 0.051\n",
      "epoch 8000: loss = -2.788, mse = 0.043\n"
     ]
    }
   ],
   "source": [
    "train(model, x_train, y_train, batch_size=batch_size, epochs=8000, step_fn=train_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "out_dist = model(x_test)\n",
    "out_dist_means = []\n",
    "\n",
    "for i in range(100):\n",
    "    out_dist = model(x_test)\n",
    "    out_dist_means.append(out_dist.mean())\n",
    "\n",
    "aleatoric_uncertainty = model(x_test).stddev()\n",
    "epistemic_uncertainty = tf.math.reduce_std(out_dist_means, axis=0)\n",
    "expected_output = tf.reduce_mean(out_dist_means, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plot_data(x_train, y_train, x, f(x))\n",
    "plot_prediction(x_test, \n",
    "                expected_output, \n",
    "                aleatoric_uncertainty=aleatoric_uncertainty, \n",
    "                epistemic_uncertainty=epistemic_uncertainty)\n",
    "plt.ylim(-2, 2)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plot_uncertainty(x_test, \n",
    "                 aleatoric_uncertainty=aleatoric_uncertainty, \n",
    "                 epistemic_uncertainty=epistemic_uncertainty)\n",
    "plt.ylim(0, 1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned in the beginning, a Bayesian neural network with a prior over weights is over-confident in the training data \"gap\" i.e. in the OOD region between the two training data regions. Our intuition tells us that epistemic uncertainty should be higher here. Also the model is over-confident of a linear relationship for input values less than `-0.5`.\n",
    "\n",
    "### Bayesian neural network with NCPs\n",
    "\n",
    "Regularizing the variational posterior $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ to be closer to a prior over weights $p(\\mathbf{w})$ by minimizing the KL divergence in Equation $(5)$ doesn't seem to generalize well to all OOD regions. But, as mentioned in the previous section, the variational distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ induces a distribution $q(\\mu \\mid x, \\boldsymbol{\\theta})$ in data space which allows comparison to a noise contrastive prior that is also defined in data space.\n",
    "\n",
    "In particular, for OOD input $\\tilde{x}$, sampled from a noise contrastive input prior $p_{nc}(\\tilde{x})$, we want the mean distribution $q(\\mu \\mid \\tilde{x}, \\boldsymbol{\\theta})$ to be close to a *mean prior* $p_{nc}(\\tilde{y} \\mid \\tilde{x})$ which is the output prior defined in Equation $(2)$. In other words, the expected output and epistemic uncertainty should be close to the mean prior for OOD data. This can be achieved by reparameterizing the KL divergence in weight space as KL divergence in output space by replacing $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ with $q(\\mu \\mid \\tilde{x}, \\boldsymbol{\\theta})$ and $p(\\mathbf{w})$ with $p_{nc}(\\tilde{y} \\mid \\tilde{x})$. Using an OOD dataset $\\mathbf{\\tilde{x}}, \\mathbf{\\tilde{y}}$ derived from a training dataset $\\mathbf{x}, \\mathbf{y}$ the loss function is\n",
    "\n",
    "$$\n",
    "L(\\boldsymbol{\\theta}) \\approx - \\mathbb{E}_{q(\\mathbf{w} \\mid \\boldsymbol{\\theta})} \\log p(\\mathbf{y} \\mid \\mathbf{x}, \\mathbf{w}, \\boldsymbol{\\theta}) + \\mathrm{KL}(q(\\boldsymbol{\\mu} \\mid \\mathbf{\\tilde{x}}, \\boldsymbol{\\theta}) \\mid\\mid p_{nc}(\\mathbf{\\tilde{y}} \\mid \\mathbf{\\tilde{x}}))\n",
    "\\tag{6}\n",
    "$$\n",
    "\n",
    "\n",
    "This is an approximation of Equation $(5)$ for reasons explained in Appendix B of the paper. For their experiments, the authors use the opposite direction of the KL divergence without having found a significant difference i.e. they used the loss function\n",
    "\n",
    "$$\n",
    "L(\\boldsymbol{\\theta}) = - \\mathbb{E}_{q(\\mathbf{w} \\mid \\boldsymbol{\\theta})} \\log p(\\mathbf{y} \\mid \\mathbf{x}, \\mathbf{w}, \\boldsymbol{\\theta}) + \\mathrm{KL}(p_{nc}(\\mathbf{\\tilde{y}} \\mid \\mathbf{\\tilde{x}}) \\mid\\mid q(\\boldsymbol{\\mu} \\mid \\mathbf{\\tilde{x}}, \\boldsymbol{\\theta}))\n",
    "\\tag{7}\n",
    "$$\n",
    "\n",
    "This allows an interpretation of the KL divergence as fitting the mean distribution to an empirical OOD distribution (derived from the training dataset) via maximum likelihood using data augmentation. Recall how the definition of $p_{nc}(\\tilde{y} \\mid \\tilde{x})$ in Equation $(2)$ was motivated by data augmentation. The following implementation uses the loss function defined in Equation $(7)$.\n",
    "\n",
    "Since we have a variational approximation only in the linear `mu` layer we can derive an anlytical expression for $q(\\mu \\mid \\tilde{x}, \\boldsymbol{\\theta})$ using the parameters $\\boldsymbol{\\theta}$ of the variational distribution $q(\\mathbf{w} \\mid \\boldsymbol{\\theta})$ and the output of the second hidden layer (`inputs` in code below). The corresponding implementation is in the (inner) function `mean_dist`. The model is extended to additionally return the mean distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_dist_fn(variational_layer):\n",
    "    def mean_dist(inputs):\n",
    "        # Assumes that a deterministic bias variable \n",
    "        # is used in variational_layer\n",
    "        bias_mean = variational_layer.bias_posterior.mean()\n",
    "        \n",
    "        # Assumes that a random kernel variable\n",
    "        # is used in variational_layer\n",
    "        kernel_mean = variational_layer.kernel_posterior.mean()\n",
    "        kernel_std = variational_layer.kernel_posterior.stddev()\n",
    "\n",
    "        # A Gaussian over kernel k in variational_layer induces\n",
    "        # a Gaussian over output 'mu' (where mu = inputs * k + b):\n",
    "        #\n",
    "        # - q(k) = N(k|k_mean, k_std^2)\n",
    "        #\n",
    "        # - E[inputs * k + b] = inputs * E[k] + b\n",
    "        #                     = inputs * k_mean + b\n",
    "        #                     = mu_mean\n",
    "        #\n",
    "        # - Var[inputs * k + b] = inputs^2 * Var[k]\n",
    "        #                       = inputs^2 * k_std^2\n",
    "        #                       = mu_var\n",
    "        #                       = mu_std^2\n",
    "        #\n",
    "        # -q(mu) = N(mu|mu_mean, mu_std^2)\n",
    "        \n",
    "        mu_mean = tf.matmul(inputs, kernel_mean) + bias_mean\n",
    "        mu_var = tf.matmul(inputs ** 2, kernel_std ** 2)\n",
    "        mu_std = tf.sqrt(mu_var)\n",
    "        \n",
    "        return tfd.Normal(mu_mean, mu_std)\n",
    "    return mean_dist\n",
    "\n",
    "\n",
    "def create_model(n_hidden=200):\n",
    "    leaky_relu = LeakyReLU(alpha=0.2)\n",
    "    variational_layer = tfpl.DenseReparameterization(1, name='mu')\n",
    "    \n",
    "    x_in = Input(shape=(1,))\n",
    "    x = Dense(n_hidden, activation=leaky_relu)(x_in)\n",
    "    x = Dense(n_hidden, activation=leaky_relu)(x)\n",
    "    m = variational_layer(x)\n",
    "    s = Dense(1, activation='softplus', name='sigma')(x)\n",
    "    mean_dist = Lambda(mean_dist_fn(variational_layer))(x)\n",
    "    out_dist = Lambda(lambda p: tfd.Normal(loc=p[0], scale=p[1] + 1e-5))((m, s))\n",
    "\n",
    "    return Model(x_in, [out_dist, mean_dist])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = create_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the mean distribution returned by the model, the KL divergence can be computed analytically. For models with more variational layers we cannot derive an anayltical expression for $q(\\mu \\mid \\tilde{x}, \\boldsymbol{\\theta})$ and have to estimate the KL divergence using samples from the mean distribution i.e. using the stochastic output of layer `mu` directly. The following implementation computes the KL divergence analytically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def train_step(model, optimizer, x, y, \n",
    "               sigma_x=0.5,\n",
    "               sigma_y=1.0,\n",
    "               ood_std_noise=0.1, \n",
    "               ncp_weight=0.1):\n",
    "    \n",
    "    # Generate random OOD data from training data\n",
    "    ood_x = x + tf.random.normal(tf.shape(x), stddev=sigma_x)\n",
    "    \n",
    "    # NCP output prior (data augmentation setting)\n",
    "    ood_mean_prior = tfd.Normal(y, sigma_y)\n",
    "    \n",
    "    with tf.GradientTape() as tape:\n",
    "        # output and mean distribution for training data\n",
    "        out_dist, mean_dist = model(x, training=True)\n",
    "\n",
    "        # output and mean distribution for OOD data\n",
    "        ood_out_dist, ood_mean_dist = model(ood_x, training=True)\n",
    "        \n",
    "        # Negative log likelihood of training data\n",
    "        nll = -out_dist.log_prob(y)\n",
    "        \n",
    "        # KL divergence between output prior and OOD mean distribution\n",
    "        kl_ood_mean = tfd.kl_divergence(ood_mean_prior, ood_mean_dist)\n",
    "        \n",
    "        if ood_std_noise is None:\n",
    "            kl_ood_std = 0.0\n",
    "        else:\n",
    "            # Encourage aleatoric uncertainty to be close to a\n",
    "            # pre-defined noise for OOD data (ood_std_noise)\n",
    "            ood_std_prior = tfd.Normal(0, ood_std_noise)\n",
    "            ood_std_dist = tfd.Normal(0, ood_out_dist.stddev())\n",
    "            kl_ood_std = tfd.kl_divergence(ood_std_prior, ood_std_dist)\n",
    "        \n",
    "        loss = tf.reduce_sum(nll + ncp_weight * kl_ood_mean + ncp_weight * kl_ood_std)\n",
    "        \n",
    "    optimizer.apply_gradients(backprop(model, loss, tape))\n",
    "    return loss, mean_dist.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implementation of the loss function uses an additional term that is not present in  Equation $(7)$. This term is added if `ood_std_noise` is defined. It encourages the aleatoric uncertainty for OOD data to be close to a predefined `ood_std_noise`, a hyper-parameter that we set to a rather low value so that low aleatoric uncertainty is predicted in OOD regions. This makes sense as we can only reasonably estimate aleatoric noise in regions of existing training data.\n",
    "\n",
    "After training the model we can get the expected output, epistemic uncertainty and aleatoric uncertainty with a single pass of test inputs through the model. The expected output can be obtained from the mean of the mean distribution, epistemic uncertainty from the variance of the mean distribution and aleatoric uncertainty from the variance of the output distribution (= output of the `sigma` layer)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1000: loss = 160.744, mse = 0.155\n",
      "epoch 2000: loss = 11.848, mse = 0.152\n",
      "epoch 3000: loss = 11.350, mse = 0.150\n",
      "epoch 4000: loss = 10.598, mse = 0.146\n",
      "epoch 5000: loss = 10.288, mse = 0.137\n",
      "epoch 6000: loss = 9.587, mse = 0.120\n",
      "epoch 7000: loss = 8.948, mse = 0.103\n",
      "epoch 8000: loss = 8.420, mse = 0.087\n",
      "epoch 9000: loss = 8.008, mse = 0.073\n",
      "epoch 10000: loss = 7.728, mse = 0.061\n",
      "epoch 11000: loss = 7.521, mse = 0.054\n",
      "epoch 12000: loss = 7.242, mse = 0.050\n",
      "epoch 13000: loss = 7.034, mse = 0.047\n",
      "epoch 14000: loss = 6.911, mse = 0.043\n",
      "epoch 15000: loss = 6.892, mse = 0.043\n"
     ]
    }
   ],
   "source": [
    "train(model, x_train, y_train, batch_size=10, epochs=15000, step_fn=train_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "out_dist, mean_dist = model(x_test)\n",
    "\n",
    "aleatoric_uncertainty = out_dist.stddev()\n",
    "epistemic_uncertainty = mean_dist.stddev()\n",
    "expected_output = mean_dist.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plot_data(x_train, y_train, x, f(x))\n",
    "plot_prediction(x_test, \n",
    "                expected_output, \n",
    "                aleatoric_uncertainty=aleatoric_uncertainty, \n",
    "                epistemic_uncertainty=epistemic_uncertainty)\n",
    "plt.ylim(-2, 2)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plot_uncertainty(x_test, \n",
    "                 aleatoric_uncertainty=aleatoric_uncertainty, \n",
    "                 epistemic_uncertainty=epistemic_uncertainty)\n",
    "plt.ylim(0, 1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that epistemic uncertainty is now high in *all* OOD regions which fixes the issue mentioned in the beginning. Aleatoric uncertainty increases with increasing x in training data regions while being small in OOD regions. This is useful for e.g. [active learning](https://en.wikipedia.org/wiki/Active_learning_(machine_learning)) where new training data should be sampled in regions of high epistemic uncertainty but low noise. The application of NCPs to active learning is described in more detail in the paper.\n",
    "\n",
    "## References\n",
    "\n",
    "- Hafner, D., Tran, D., Irpan, A., Lillicrap, T., and Davidson, J. [Noise Contrastive Priors for Functional Uncertainty](http://proceedings.mlr.press/v115/hafner20a.html). In *Proceedings of The 35th Uncertainty in Artificial Intelligence Conference*, pages 905-914, 2020.\n",
    "\n",
    "- M. Gutmann and A. Hyvärinen. [Noise-contrastive estimation: A new estimation principle for unnormalized statistical models](http://proceedings.mlr.press/v9/gutmann10a.html). In *Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics*, pages 297-304, 2010.\n",
    "\n",
    "## Acknowledgements\n",
    "\n",
    "Thanks to Danijar Hafner, Dustin Tran and Christoph Stumpf for useful feedback on a earlier draft."
   ]
  }
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